What's her game here?

I'm in a weird situation with my ex, and I'd like to have some perspective on what's going on in her mind. I'll be providing the details of what went on between us, but feel free to skip ahead to the main point at the end of this post.

Basically, we were in a very short relationship that ended half a year ago due to her not feeling ready for a relationship on her part (at that point in her life, she'd never been with another man besides me, and she hasn't been with anyone else since). After the break up I started chasing her very hard and it soured our relationship to the point that we didn't talk to each other for a few months.

By that point, while I'd still get back with her if I had the chance, I'd started dating other women and she's no longer my 'priority' so to speak. Anyway, we met up again two weeks ago because we had mutual friends, and since then I've been confused about what she wants out of our friendship. At first, she didn't even speak to me and practically had to be strongarmed by our friends to greet me.

After that, we just started talking normally but every now and again she'd grab my hand and start either scratching me or biting me. That aside, when we met last week, she kept punching me on occasion and ended up scratching out a tic-tac-toe game on my arm once. Now, I don't particularly mind it, and I'll admit I have a slight fetish for getting bitten but I've got about five scars on my hand at this point thanks to her. A friend of me said something along the lines of that meaning that she wants my attention but I'm not so sure about that. I say this mostly because when we were offered a picture together, she immediately rejected the idea in favor of getting other people in the picture as well.

We met a week after that (that is, a few days ago) again as part of a Society meeting, where things got even weirder. She still keeps trying to scratch and bite me although she did other things as well that make me very confused about her intentions. For one, when I started flirting with another girl in the Society, she started getting catty with me and tried to drag my attention away from her. Then when she had to sit in a seat next to me, she asked me to move to the next one so we wouldn't have to sit together. Then she stole my bag and decided to name her team (long story) after it, all while claiming that it was a better version of me. Then she shared her drink with me when we moved at the bar, but started punching me when I almost finished the glass. Then she ended up talking to another guy for somewhere between half an hour to an hour which I admit made me exceptionally jealous, although a few of my friends said it didn't look as if anything came out of it. Then she dragged me away from another girl I was flirting with to tell me she was leaving but when I offered to go to the bus station with her, she said she'd take the cab.

Anyway, that's where we left of, and I suppose the question I want to ask is:

What's going through her mind with all these mixed signals she's giving and should I just avoid her if she's being this indecisive at this point?

JianGeGe, she bites, scratches and punches you. She drags you away when you speak to someone else. She stole your bag. Seems to me that she has the social skills of a toddler.

Find a woman who can behave like a grown up.

I'm with @basileandthyme. This is not a woman; this is a child and a disturbed one at that. WHY would you even want any kind of relationship with a person like this - why would you even think that you could have a real relationship with a person like this? Even if you have a biting fettish during intimacy, all that crap that she's doing is in public. I would find it embarrassing and irritating. Is that really the kind of woman that you want?