Does she want to be with me?

Sounds like mostly good news if it's verbal abuse but no physical or sexual abuse. Cutting is much less problematic. Cutters tend to have a hard time understanding their own feelings. So when she feels upset because can't fully understand it or calm down, cutting is an effective way to let the emotion out, a non verbal way of venting (plus it kicks the endorphins in if the cut or cuts are strong enough).

It's an inner turmoil, which I'm sure you've figured out already. I do think that her willingness to have sex with you followed by her pulling back, shows that she has feelings that she isn't comfortable with. Now we know that anytime you fall for someone there's a mixture of excitement and fear. My guess is that she feels that energy and is uncomfortable with it. Unlike the feelings she had for her shitty ex (which were likely minimal and bland and he was likely one of those types where it could have been him or anyone else she'd seen at that time) which matched her esteem issues you're triggering an actual conflict within her.

And that fits with her not saying anything bad against you. My sister told me that life sends the same challenge at you in different forms until you get it right and get past it. It seems to me that to get this girl you'll have to get her talking and then help her unravel the emotional knots. If you can get her talking about a past relationship, the kids, a job opportunity, etc. something in which she clearly had a chance to make her life better and instead shot herself down you might be able to get her to see how her self-image and self-defeating patterns factor into her decisions in life and with you. I'm sure she "knows" she's made some bad choices, but there are levels of knowing (like a cigarette smoker who knows it can hurt him, but he doesn't really know until that cancer diagnosis is made - that's bone knowing, soul knowing).

Take care of yourself. The darkness doesn't voluntarily give up its prey. People in pain will, like a drowning person, fight you instead of letting you take their hand and lead them to safety. It might be Thanatos. I don't know, but these type of things are tough. I don't, however, think it has to do with her not caring about you. If anything, it's the opposite.

"Wait for everyone to go away
And in a dimly lit
room where you've got nothing to hide
Say your goodbyes
Tell yourself we'll read
a note that says
I'm sorry everyone
I'm tired of feeling nothing goodbye
Wash your face
Dry your eyes
Cause you've been waiting a long time
You've been waiting a long long time
To fall down on your knees
Cut your hands
Cut yourself until you bleed
But fall asleep next to me
Have a dream I'm falling down
On my face
Scrape my knees
Scrape my hands until they bleed
Cause you're fast asleep next to me
Next to me."

It seems to me that the real difficulty is her underlying emotional and psychological composition. My guess would be that she does have feelings for you, but that intimacy (especially true intimacy) is not something she is comfortable with.

Many strippers have a history that includes sexual abuse of some sort and that tends to be one of the things they bring with them, along with a tendency to use men and sex (or sexual acts) to punish themselves for feelings of guilt and to manifest their own self-hatred in reality. So she is comfortable with the past crappy boyfriends because they fit in with her own mental image.

I think there is a part of her that values you, but there's an internal hangup that she would have to be committed to overcome.