I think she's trying to find out how much you care for her.
The thing is, we aspies don't give off the right signals, which means that we can be in love with someone and think our love is clear when actually it's not at all. I reckon she was interested at first, but because of the wrong signals, she's not at all sure how much you like her.
I don't like the sound of the head games, but without knowing her I can't judge whether she's being manipulative, or whether she just has her own insecurities.
If you like her, and don't think she's being deliberately manipulative, try setting up a long date together. Maybe include a nice dinner and see if you can talk to her about it, and see if you're on the same wavelength. Don't delay, though, because it sounds like she's uncertain and you might lose her.
Long term, if she's insecure, you'll need to be careful that you are capable of providing the amount of attention she needs, and that she knows your AS limitations, but I wouldn't worry about that right now. If you're interested, just show her that, and see how it goes.
Not that I know much about romance, I might have got it all wrong 