My dtr is asperger - so a little different but some of her behavior is my dtr as well haha. I'll address the behaviors I have experience with.
I am very clear on rules and consequences - there is no next time. If I'm not clear and I realize it after the fact - it's a done deal, I let it go and remember it for next time. It's how she works. Everything is routine, so if it happens once, you can bet its routine . . . like I will not drive her to school or pick her up because I can't do it everyday and she would drive me absolutely insane asking . . . my husband on the other hand (he works away, so isn't home everyday, when he is home he picks her up EVERY time, he doesn't care which is fine, but I can't do it everyday).
I don't engage in banter, button pushing or losing my cool with her. She will not get out of my face and go to her room when she's upset, she's very confrontational, I, as the adult, have to remove myself from her presense. I go to my room, shut and LOCK the door or go to the bathroom . . . once she was screaming and knocking on the door for 20 minutes straight . . . but she hasn't done it again because she didn't get a reaction. It's hard, but I refuse to let her control our family. Which means I bite my tongue and move on.
Chores - haha, haven't figured this one out yet. But, I am prepared to do anything I ask her to do because she probably won't do it. And if she does, it would be 3 days later. I ignore the anger when I ask her to do something, I give a time frame and if she doesn't do it, I will - end of story, no fight. I have a "star" system which is magnets on the fridge. When my girls complete a chore or do something I ask, they get a star by their name. Stars can be worth a number of things - whatever motivates them - this summer it was a trip to the zoo, so when the both got X # of stars we went to the zoo. Or to a place they want to eat, a movie, or cash. This particular daughter is 15 and my next one is 7 . . . my 7 year old will try to help her get stars, letting her do the easy chores, almost begging her - it's cute and sad at the same time. I pay my 7 year old a whole lot more than I pay the 15 year old and her stars aren't worth near as much!!
She used to eat like your daughter - it was so frustrating. We went gluten free 5 years ago and it's made an incredible difference in her behavior, but she's still quirky - but food is no longer an issue.
It makes me sad when you say you are two people just not meant to be together - you just have to rise above her and be the adult (trust me when I say this - this is from experience). Walk away, don't give in, it's hard trust me but it will help her. Right now you are spoiling her, giving in. You have to be tough, I don't know how many times I've cried myself to sleep feeling horrible because I know she is different than me and thinks differently and it breaks my heart that she's so out of control. She won't like it at first, and will push your buttons even more, which is even more reason to be your "pleasant" self. It's taken a lot of work and I'd say we are in a better place, her behavior no longer rules our family, she's not in charge - I am.
You should read "Parenting with Love and Logic" - it's really helped.