Poor girl I'd definitely let her set the pace of things... she won't trust you, and if you push too much she'll withdraw and trust you even less. Try more verbal assurances and affection, and verbally offer things like hugs where she has the option to decline or accept.

Like... I never went through that sort of abuse, but I do have a lot of various symptoms of trauma. If someone touches me unexpectedly, I cringe, freeze, and/or panic. Sometimes I'll even lash out verbally "GET AWAY" or "DON'T TOUCH ME!" (I've learned to surpress that pretty good).

If she doesn't want you to make food for her, you could try making things together. Ask her if she'd like to bake cookies with you, or make your own personalized pizzas together.

Can she read, and do you have books that she can read? You could always have reading time where you're both in the room reading together, but you not reading TO her if she doesn't like that (could also offer a colouring book she can use, and you can read near her and occassionally stop to chat).

How is she when it comes to bath time? I can't imagine that she's comfortable with you in there to wash her hair based on the things you've said. If she struggles with having you anywhere near her naked body, you could see if she'd want to have a bath with a swimsuit on (it would make her feel less exposed).

What does she like to do when she's on her own?