I've been picking up the pieces (And trying to put them together)

Head-cannons

• Loved the way that the book showed the final battle with Voldemort, but always wondered about the possible blow-back of talking about the Hollows and Horcruxes openly. He literally admitted to being the master of the Elder Wand in front of dozens of people. So I'm going to pretend that, once she got over the shock of Harry being alive, Hermione cast Muffliato over Harry and Voldemort so that all the spectators could hear was a buzzing noise, but since she wasn't part of the conversation the spell went a bit wonky. People have figured out that the whole thing had something to do with love magic and the wand choosing the wizard but no specifics. As a result there are a lot of - interesting - theories on what happened.
• Dedalus Diggle becomes DADA Professor and Head of Gryffindor after the war (he passes the responsibilities as Head to Neville to free up time for his research into experimental magic and defensive counter-jinxes).
• Standard Auror Training
  • Year 1 (Hit Wizards are considered qualified after completing mandatory classes, 1 elective, and 50 hours on-the-job raining such as ride-alongs) (Aurors are required to take all mandatory classes and 2 electives in their first year)
    • Mandatory 
      • Advanced DADA (+practical duelling/fitness)
      • Magical Law
      • Wards and Enchantments
      • Crime Scene Protocols
    • Mandatory for Aurors
      • Field Healing
      • Advanced Potions
    • Electives
      • Advanced Dark Objects and Curse Breaking (Hit Wizards in this track are qualified to classify any seized items to be sent onto the appropriate department or handle XX level dark objects i.e. is this cursed enough to need actual Curse Breakers (XXX-XXXXX level), or is it an object that should be sent to the Unspeakables)
      • Advanced Muggle Studies (Hit Wizards in this track interface with the Misuse of Muggle Artefacts and Muggle-Worthy Excuses departments)
      • Field Healing (Mandatory for Aurors. Essentially Wizarding first aid/CPR)
      • Advanced Runes and Ciphers (Hit Wizards in this track rarely go out into the field. (Required for Aurors specialising in Intelligence but can be taking in any year)
  • Year 2
    • Concealment and Disguise
    • Basic Formations and Operation
    • Advanced Flight Ops (Optional. Prerequisite: Flight Test)
    • Basic Flight Ops (Biweekly for weak flyers; Bimonthly if you pass the Flight Test)
    • Abnormal Psychology
    • Occlumency and Legilimency
    • Resistance to Potions and Enchantments
    • Advanced Magics
  • Year 3 (Trainees take part in simulated scenarios)
    • Specialisation
      • Intelligence
        • Advanced Runes and Ciphers
        • Analysis, Application, and Effects of long-term strategies
        • Surveillance Charms
      • Field
        • Advanced Duelling
        • Advanced Field Healing
        • Theory and Application of Battle Strategies
• The Auror department waived the requirement that Trainees must complete all three years of training before being allowed in the field for three years. They only accepted new members that were veterans of the Battle of Hogwarts (mostly members of the DA) that had the required OWL qualifications or could otherwise demonstrate competence. All trainees completed an abridged version of the program with less classroom time. They eventually returned to the Standard Training program and returned to requiring NEWTs to apply. 
• None of the kids know what the Golden Trio were doing during their seventh year beyond what the History textbooks say. They do know its the reason the three of them refuse to go camping.
• Albus thinks Harry refuses to step foot in Malfoy Manor is because he's a prejudicial git. But its really because he can still hear his best friends' screaming and the weight of Dobby's body.
• Percy spent the war passing information to the Order through Aberforth. (he's the one to tell Percy about the final Battle) He does his best to weaponize bureaucracy to protect Muggleborns. (That's how he meets Audrey. She's one of the Muggleborns he got off the Ministry's radar. The two of them collaborate on a sort of underground railroad.)
• Percy was a hat-stall between Slytherin and Gryffindor. In the end the hat sorted him into Gryffindor because "it takes a great deal of bravery to stand up to our enemies, but just as much to stand up to our friends" or in his case family.
• Harry and Ginny live out in the country, but they let everyone think they still live at Grimmauld Place in London (Keeps the reporters away)
• Fireplaces can have separate Floo connections. For example, some people could only be able to Floo into the formal parlour and can't come through without permission. Close friends/family can Floo into the kitchen/informal part of the house at anytime (All the fireplaces at Hogwarts are on the same connection except for the Headmaster's office. That's how Umbridge was able to try and grab Sirius. Its like when two phones are on the same line and you can hear the other person's conversation)
• Harry introduced the idea of using the Taboo for a distress signal for Aurors. Its tied to the person similar to the Trace so that people can't accidentally activate it. (Gives backup teams a location to Apparate to. Very few wizards are capable of casting advanced enough protection to avoid them failing when a Taboo is triggered.
• The Marauder's Map only shows Mooney, Padfoot, Prongs, and Wormtail when one of them unlock the map. Essentially, the map doesn't let everyone access all of its features. The Marauder's have full admin privileges, Fred&George have the least amount of access (they only see a map of the castle and no names explaining their comment that they've memorised the map already). Harry is somewhere in the middle but Sirius and Remus give him, Ron, and Hermione full permissions.   
• The Taboo cannot break the Fidelius Charm or Blood Wards, but it can provide a general location (Harry could say Voldemort at the Dursleys and Grimmauld Place without the protections falling. The Death Eaters knew to watch Grimmauld Place but the protections)
• Harry goes into Hogwarts as a guest lecturer a couple times a year
• Because of the events in the Room of Requirement Harry decides that all Aurors need to at minimum contain Fiendfyre if not put it out.
• Hit-Wizards are the equivalent to a wizarding police force. Aurors are closer to military/intelligence.
• Teddy Lupin was a Hufflepuff and became a Healer after Hogwarts. He's primarily a researcher focusing on treating Werewolf bites and is married to Victoire. (They may or may not have eloped :))
• I can't imagine Luna and Rolf having a traditional wedding. I can imagine something like cross between "we would go together to the heart of the beech woods,--and there, under the green arches that would be like a splendid cathedral, we would be married" (Anne's House of Dreams) and the "how i love being a woman" scene in AWAE. 
• Next-Gen Houses
  • Victoire (Ravenclaw), Dominique (Gryffindor), Louis (Hufflepuff)
  • Molly II (Ravenclaw), Lucy (Ravenclaw)
  • Fred II (Gryffindor), Roxie (Gryffindor)
  • Rose (Gryffindor), Hugo (Hufflepuff)
  • James (Gryffindor), Albus (Slytherin), Lily (Gryffindor)
• Rose and Scorpius have a similar dynamic as Harry and Hermione. Poor Albus keeps alternating between being jealous that his "best friend" and his best friend hang out without him and loving that his family like his boyfriend.
• Since people tend to be brave and loyal and ambitious and intelligent the sorting is much more complex. Like is it bravery or loyalty that makes you stand up for a friend against the world. Wouldn't it be brave for someone to take risks to achieve their ambitions? Unless you absolutely don't have a certain characteristic (Crabbe and Goyle could never be Ravenclaws) the hat looks at which traits you value. It then puts you into the house that would best address your values.  
• In the years after the war the House rivalries become less intense. The whole narrative around Slytherin house started to change as instead of the most famous graduates being Death Eaters, they started having graduates using their ambition to succeed in fields other than the Dark Arts. By the time the next-gen kids go there it's more fun teasing rather outright hostile. Like I can imagine James/Fred turning all the Slytherin ties red before a Quidditch match; I can't imagine them getting to the level of maliciousness of some of the James/Snape or Harry/Draco interactions. 
• The Lightningbolt Series of brooms are named after Harry, but the company refuses to admit it. They also got Ginny to advertise them by making a sponsorship deal with the Harpies. But they are really good brooms though.
• Instead of living in the country-side or in wizard-only areas like Diagon Alley many younger witches and wizards bough homes in muggle towns and took precautions to prevent people from noticing the magical nature of their homes.
• Dementors effected Harry more than the others in third year because of the Horcrux. They could sense that he had two souls inside.
• The memory of the Halloween that James and Lily were murdered was partly Voldemort's.  That's why he couldn't see the Thestrals until fifth year, he wasn't really old enough to understand that Lily had died. 
• Harry is scared of dementors because they make him feel useless. Its less about being afraid of fear and more about being afraid of being paralyzed by fear.
• Once the Horcrux is removed Harry's worst memories rotate between the graveyard, Sirius, and Fred.
• For a brief time after the Battle of Hogwarts his Boggart changes from a dementor to the people he cares about blaming him for not giving himself up quicker (effects of survivor's guilt)
• I refuse to believe that Harry and Ginny are bad parents. Like their not perfect because that's boring but they try.
  • James feels a little ignored once Al starts Hogwarts. H&G focus more on Al since he's obviously struggling and think that James is fine since he's getting good grades, has tons of friends, and hasn't locked himself up in his room to become a child of darkness. Basically James has a mild case of "oldest child syndrome."
    • James would see the same thing as Ron in the Mirror of Erised. Except where Ron feels overshadowed James feels like he has to live up to an impossible legacy. 
  • Al's a little easier to pinpoint. He tries so hard not to be Harry that he ends up being exactly like Harry. A big issue in his and Harry's relationship is that Harry won't just be honest with him instead of trying to protect him and that they both have the ability to say things things in the worst possible way.
  • Lily's just bidding her time until she can join the Aurors and prove that she's not a little girl. I totally see Ginny being an overprotective mother.  
• Gideon and Fabian are Irish Twins and younger than Molly.
• Molly and Arthur are at least 10 years older than the Marauders and Bill is about ten years younger.
  • Bill, Charlie, and maybe Percy are actually old enough to remember the first war.
  • Molly and Arthur didn't join the OoP the first time because they had 3-5 kids that weren't even old enough to go to Hogwarts. The second time around only Ron and Ginny were underage, but at least halfway done with school, and in the worst case scenario had 5 older sibling to take care of them.
• Sirius and Remus were only in their thirties in the books.
• Regulus leaves school after 5th year and joins the Death Eaters.
• Snape's memories were biased because I can't imagine Lily falling for the boy that bullied her best friend unless Snape and James were as bad as each other.
• Snape barely earns the "not as much of a jerk as you could've been" award.
• James and Dudley have similar character arcs.
• Rough Marauders timeline
  • Fifth year
    • Beginning: All three manage to complete the Animagus transformation. They start making the map.
    • Middle: James rescues Snape from Werewolf!Remus
    • End: Snape's Worst Memory (SWM) events
  • Summer: Sirius runs away
  • Sixth year
    • Beginning: War tensions are higher
    • Middle: James finds out his parent's health is declining (maybe over Christmas)
    • End: Uncle Alphard dies
  • Seventh year
    • Beginning: One of Lily's parents die
    • Middle: James and Lily get together
    • End: Marauders + Lily join the Order 
  • After Hogwarts
    • Petunia and Vernon's wedding
    • Lily's other parent dies
    • James and Lily wedding
    • James's parents die of Dragon Pox
• I don't think that Lily hated James. She actively disliked him but the two of them probably ran in the same circles and most likely had friends in common. However, she did hate Snape's friends who are explicitly stated as using Dark Magic on Mary MacDonald.
• Lily and Snape were best friends till 2nd year. As Lily made more friends at Hogwarts she had less time to spend hanging with Snape leading him to spend more time with his fellow Slytherins. Considering neither got along with the others friends they really only spent tons of time together over Summers. I feel like Lily spent a lot of time defending Snape to her friends + trying to get him to see that his friends were bad influences and the Mudblood incident drove home that she can't "fix" him.
• My interpretation of the werewolf incident:
  • James/Sirius/Peter figure out Remus is a werewolf in 3rd year. Snape is the only one obsessed enough to notice that Remus is always "sick" on full moons and theorises Lupin is a werewolf. All the other students either don't think about it enough to notice the pattern, believe that Remus really has a sick relative that he visits, or thinks he has a badly behaved rabbit hidden in the dorms.
  • Snape catches Sirius doing something while sneaking around sometime during 5th (Headcanon: He was trying to convince Regulus not to join the Death Eaters/stop listening to his parent's propaganda). The two of them fight. Snape tries to goad Sirius into confirming his theory. Sirius lets slip the knot on the Willow information.
  • Snape figures the only way to confirm his theory is to catch Lupin on a full moon. If its true he can get at least one of his enemies expelled.
  • The Marauders are in the Shack waiting for the transformation when a cooled off Sirius mentions he told Snape about the Willow. James realises that Snape is obsessed enough to come look. He manages to stop Snape but not before he saw Lupin transform.
  • Dumbledore makes Snape take some type of vow not to mention that Lupin is a werewolf to anyone. That's why he doesn't just tell Lily and tries to lead her to the conclusion on her own.
  • Snape attacks James with a cutting charm (early variation of Sectumsempra?) first in SWM. He's probably understandably worried that the Marauders would try to get "even" with him for almost exposing Remus and jumpier than usual. Basically, both Snape and James are in wrong.
  • I think it says something that Snape's first instinct is to hurt James, and James's is to humiliate Snape.
• James's parents start to decline health-wise his sixth year + the threat of leaving the safety of Hogwarts for a world where Voldemort is becoming more powerful (Plenty of his classmates have joined the Voldemort Youth) forces James to mature. He realises that he has to be an actual adult now and stops being a bully to Snape/Slytherins. 
• Snape on the other hand still tries to go after the Marauders.
• Tobias Snape didn't find out about magic until Snape started doing accidental magic.
• Cokeworth is an old English mill town. Snape's family is extremely poor, his father is most likely a factory worker of some kind. I could see how finding out your wife could do anything she wanted with a wave of her wand and didn't do it would be a hard pill to swallow for Tobias who probably grew up poor himself. I could imagine the Snape's parents probably were pretty neglectful and his father finally crossing over to abusive after finding out about magic + the decline of industry.
• Lily and Petunia most likely grew up middle-class. I could see her father as some kind of office worker whose job was probably not as intertwined with the state of the mill. Maybe her mother worked as a nurse before getting married and returned to work when the mill started declining.
• Hogwarts students have they're own type of "public school accent".
• Petunia was a secretary and that's how she met Vernon. She also definitely pretended to have a posher accent than she really did.  
• James and Lily become friends over the course of sixth year and start dating their seventh. 
• I've got two scenarios.
  • Lily's parents die in a car crash or something sometime between Petunia's wedding and her's.
  • A more complicated timeline assuming Petunia is 2-3 years older than Lily. One parent dies of suddenly sometime in 6th/7th year. The other parent has some kind of illness leaving a newly adult Petunia as primary care-giver while Lily is still attending Hogwarts. That parent keeps trying to get Petunia to fix things with Lily (I don't think the Lily/James/Petunia/Vernon dinner or Lily being invited to the wedding would have happened otherwise). Parent dies after Petunia's wedding but before Lily's.
  • I like the second version more because I think its weird to have all couples die at the same time as each other (Potters I,  Potters II, kinda the Longbottoms, Lupins). Makes Petunia a more complex character and not another person stuck on a dumb childhood issue. Petunia being bitter that Lily went off to Hogwarts while she was watching a parent decline. And then constantly "taking Lily's side" despite her being the one that's there makes more sense. I think they did start working through things after Lily's wedding since Petunia knew about Harry/Lily mentions Petunia sending a Christmas present. 
  • The Dursley's are still horrible people but up until Lily's death there was still some chance of growth. (They were officially irredeemable when they put their baby nephew in the cupboard).
• James's parents die of dragon pox within days of each other after the wedding but before Harry is born.
• Dudley's kid either marries a wizard or has a kid with magic.