I think all 3 responses are right on. When she says, "I saw the hairs on your sex," it's a withering put-down and at the same time an expression of complete intimacy and connectedness.

I think there's also aggression in that encounter with her mother, because E. is breaching the boundary in one massive way (incest is taboo in almost every culture) and one big-ish ways (even industrialized nations are still iffy about same-sex couplings). Note that I'm not saying she was attracted to, or was trying to have sex with, her mother; rather, she used a symbolically laden way of expressing her aggression more evocative than, say, breaking dishes or slapping her mother.
"All you need to start an asylum is an empty room and the right kind of people."

I think the scene with her mother was just her extreme loneliness. She just wanted affection from someone, anyone, but because she has some screws loose that was difficult to find.

No she was not a lesbian. The relationship with her mother was not exactly healthy. She was emotionally repressed all her life.
She also has no sexual experience, so her emotions just get mixed up.
I think that scene in bed was just a subconscious desperate attempt to tear down that wall between her and her mother, and around herself.