My suspicion is that we're all dead. This isn't time travel, it's Purgatory. At least some of the students are being tested (hence why your character is being steered towards either choosing corruption/lust or love/compassion). Essentially, Heaven and Hell are playing a game to see which side you'll be swayed in the end. Mrs. L is pretty clearly either the Devil or just one of Hell's demons (it's L for "Lucifer", and her address in the exercise tape ad is 666). The mysterious person texting our phone and who keeps arguing with her is clearly on the side of good (based on the stances they're taking and what their intentions seem to be).
It's hard to tell at this point exactly which characters would be the real people getting tested and which are just actors/facsimiles meant to act as testers/temptation/influencers, but unless this is a Purgatory solely for one person (the player), Isabelle definitely seems to be the most likely candidate to be a fellow lost soul.
Lindsay's probably the next most likely person to be real and not an "actor". Maybe after that Flora and/or Kate. I suspect everyone else is part of the test, working for one of the two antagonistic sides.
The Nurse might be another person being tested though. If we assume the indicator for a lost soul is that they're someone who has flaws we can help them overcome, she's basically got an inability to tell people no. She pretty much admits this, and we can encourage her multiple times to stand up for herself against Kate. Her redemption arc would basically be learning to take charge for once.
Her arc has basically been that she became the paragon she is because of her parents pushing her. She mentions they got her into running, and it seems likely that she's such a good student because they push her to be. She also mentions that her parents wouldn't be happy if she had a boyfriend.
You can tell her in a couple different scenes that she needs to learn to stop trying to live up to what other people want her to be and just be what she wants to be.
If she's injured to the point where her future athletic career is ruined, that forces her to reevaluate all her priorities.
From there, how we interpret that depends on whether or not she's another soul being tested or just meant as a test for you.
I'm not sure it is the same person.
We're basically told that Maxine essentially drugged Lindsay, which made her suggestible. "Mer" (the mysterious person manipulating things for "Good") then influenced Lindsay into stealing the chocolates, to set into motion the chain of events where you become the hero (bringing you and Isabelle together). But presumably Lindsay remains in that state (or can be triggered back into that state again), which would make it entirely possible for someone else to take advantage of it.
When you arrange a meeting with "Mer", you get to eavesdrop on a conversation between them and Mrs. L. Once they start talking about Mer's manipulation, and Mer points out they're only prohibited from direct manipulation, Mrs. L replies with "Oh, this is how you want to play it?" Which very much suggest she's going to take an even more active role (in a "two can play that game" sort of way).
In other words, I think it's pretty likely that Mrs. L is the one who encouraged Lindsay to hurt herself, as part of her own scheming.
The alternative is Maxine. She seems to either be a neutral party of sorts or an agent of chaos in some way, and might have her own agenda. She's also the one who stole the locker, not Lindsay/Mer. And Maxine is definitely aware of what's really happening, regardless of how she's supposed to be part of it.
The fact that she wasn't part of the original timeline originally led me to believe she might have been the angel steering you towards good while Mrs. L steers you towards evil.
As the game goes on, I suspect she's someone else in Purgatory with you, who has her own issues she needs to sort out. Specifically, her pent up anger and issues tied to her sister and bullying. If she's being tempted, it's not the Love/Lust dichotomy you're facing, as much as she's being forced to choose between letting rage and vengeance consume her, or finding a way to let go of her hate and instead embrace the happier things in life (like the love of a young boy, for example).
If you tend to go the Love route over the Lust/Corruption route, you start to notice that each of you is making the other better (in the scene in your bedroom after kidnapping Maxine's cat, Isabelle has a line about how it feels like you're the only one who understands her, and you always know how to make her feel better. You respond by telling her that you've always had problems being social but she makes it easy for you to say what you feel because she doesn't judge you for it). At one point you straight up tell her that she's a good person because she cares about making things better, but her flaw is that she can go too far - and that's why you have to be there to tell her when to stop. In other words, you're showing her how to be a better person and not let her love of justice turn into vengeance, while she in turn is helping you come out of your shell and possibly learn to love and not just be a sex-crazed loser.
...which is why Mer pushed the two of you together by manipulating Lindsay. While the two sides are apparently forbidden to interfere directly (the test seemingly being throwing you into a situation where temptations abound and seeing whether you sink or swim on your own), by manuevering the two of you together Mer has created a scenario where the two of you together are better than either of you would ever have been alone.