**Continuation of ACs spoilers***
I understand your questioning some of the plot elements and while I can see how some could be explored, I think others are an extension of Nina's own lack of perception and self-awareness. Honestly, I prefer the demands the film makes on analysis rather than simply handing the audience the answers. Here are my thoughts to your questions:
Why do the other dancers in the company dislike Nina? Two reasons I felt were quite obvious:
Jealousy - They are all fighting for the same spot and based on the audition we saw (and the dancers saw), there was no evidence Nina was the clear choice for the role.
Nina's personality - There was no hint of kinship between Nina and the rest of the company. If anything, there were hints of animosity (like the girl who didn't get the role).
Why is Lily drawn to her? It seemed to be her personality. She was new and trying to warm up to the new star and break her out of her shell. Her visit to their home was enlightening because Lily could see some of the circumstances in Nina's home life, which made Nina a very sympathetic character to Lily. I've known LOTS of Lilys in my life. Hell, I've BEEN a Lily a few times. But more often, I'm a Nina.
How does her history of self-mutilation relate to what she is going through and what is happening to her? I thought that was ultimately clear by the end of the film. Aronofsky drops subtle hints here and there, especially through the scenes with Nina and her mother. The final scene with the two of them reveals the most. I kept looking for the "trigger" that would set off one of her fugues, but I couldn't quite get it. And maybe it's not supposed to be obvious to us. But it does make me want to see the film again.
Does she actually have sexual feelings towards Lily (and women in general)? I believe it wasn't clear to the audience because it isn't clear to Nina. We were simply voyeurs in her sexual exploration.
To give a further example: the scene where Erica almost throws away the congratulatory cake that she buys Nina is basically the only moment in which we get a concrete look at how unhinged she might be, and yet we're supposed to believe throughout the film that she is a potentially dangerous character. I love that you brought this up because I thought it was brilliant atmospheric expression and it clued me in to the film's point of view. We are sort of led to believe Erica is more dangerous than she is because we are seeing her through Nina's eyes. The paintings and the cake give us a hint at the level of instability and obsession that has passed from mother to daughter, but they manifest themselves in different ways in both characters. Erica may push her daughter to become what she never was, but at the same time, she knows what triggers her daughter's self destructive behavior and tries to protect her from it. Nina often confuses her mother's protective nature with stifling and overbearing parenting, but we really don't understand this until the last act of the film.
Why did Aronofsky never do anything with the myriad paintings that she has done of Nina? That's a good question as it could go either way. It was interesting to see how the paintings changed during Nina's fugue state. I think they were a symbol of the destructive codependency in the household. The stress and obsession that exists within both of them that continually fuel each other until they surface in self-destruction.
This discussion just reinforces my support for this film. It's not by the numbers and it requires a bit of effort from its audience. Some people may not like that, and that is okay, but I really love this about the film.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian