To Dwell on Dreams
Right from the get-go, Delphi makes a much better impression upon Harry than Draco does. For one, she actually bothers to ask his name! And both she and Draco are fascinated by him immediately; they both bet that they're the one who'll be able to get the famous Harry Potter to be their friend. (Draco fails, but Delphi succeeds--though not on terms they'd expected. She befriends Harry by aligning herself with Gryffindor, which Draco insists is not in the spirit of the bet.)
Delphi's issues with the other Slytherins start pretty much immediately. She becomes a target because of her weird friendship with Harry and Ron, and all the bullying doesn't make her want to be friends with those Slytherin assholes, either. Because while she was raised in hatred and bigotry, Hermione Granger in particular breaks her of her prejudice. That a Muggleborn girl is the only one who can match her shocks Delphi, and her interactions with Crabbe and Goyle go a long way towards convincing her that blood status is not at all a real marker of a wizard's worth.
At first, Delphi tries to simply ignore the rest of the Slytherins. She did her best to make up with Draco after they snub each other, but when he isn't particularly receptive to her attempts to appease him, the other girls descend upon her like wolves. Suddenly they aren't willing to let her hold her silence around them; they think they smell weakness, and so they start to poke and prod at what they hope might be sensitive spots. Delphi is mostly unaffected by this attempt at bullying, but it's certainly a contributing factor in her eventual decision to join the Gryffindors instead.
In her first Potions class, something occurs to Delphi that never occurred to her before. As Snape says, there is very little "foolish wand-waving" in potions-making, and so some wizards hardly even consider it magic. So, Delphi wonders... Could Muggles and Squibs make potions, if they had access to the ingredients? Delphi stays behind after class to ask him, and he's so shocked that she's thinking anything about Muggles other than "kill 'em all" that he awards her a point to Slytherin.
It creates quite the scandal when Delphi outright abandons the Slytherin table to join her Gryffindor friends during meals. And somehow word of her increasing reputation as a blood traitor gets back to Madame Lestrange, leading the old woman to send a Howler that threatens Delphi with disownment if Delphi doesn't immediately cease being friends with the three most egregiously awful candidates in the school (Harry Potter, a Mudblood, and a Weasley). (For peak embarrassment, this Howler may or may not go so far as to threaten that she'd better not "spread her legs" for any of them.)
After the incident with the Howler, Quirrell interrogates Delphi about her friendships. Voldy doesn't give too much of a shit about Ron, but her rationale for befriending Harry and Hermione intrigues him. She argues that Hermione's blood status shouldn't matter, considering how innately talented a witch she seems to be. And as for Harry Potter... befriending him is obviously advantageous. Why wouldn't she, since she can?
Quirrell starts keeping Delphi after class, not-so-subtly giving her access to things that she almost certainly shouldn't have access to: particularly, advanced books full of dark magic (A Grimoire of the Dark Arts, Magical Domination, Secrets of the Serpent Tongue, The Oft-Forgotten Arts). She's thrilled to have them, right up until Snape interrogates her about what's going on and confiscates one of the books. (After this theft of materials, Delphi gets the idea for her book network.)
Canonically, Harry starts having nightmares about Voldemort after seeing his parents in the Mirror of Erised.
When Ron realizes that Draco had the book in which Ron hid the letter from Charlie, Delphi braves the risks of returning to the Slytherin Common Room in order to get it back before Malfoy sees. (She succeeds in preventing Harry and Hermione--and Neville and Draco--getting caught.)
The detention in the forest involves Harry, Ron, Hermione, Neville, Delphi, and Draco. The groups end up: Hagrid, Ron, Hermione, and Neville; and Fang, Harry, Draco, Delphi.
I want Neville to come along for the "descent into the underworld" bit. The protections should map to each of the kids, save Quirrell's false protection. Fluffy is Delphini (he is associated with the Underworld, she with death); Devil's Snare is Neville, who's gifted when it comes to herbology; the flying keys are Harry, who's an amazing seeker; the chess is Ron, who's very good at the game; the logic puzzle is for Hermione, who oddly has a lot in common with Snape; and the Mirror of Erised was probably meant to stop anyone who found it. (Did Dumbledore really think it was guaranteed that Harry wouldn't have wanted to use the Stone?)