Hey Jamse,
First off, the disclaimer: I have absolutely no experience with small children, apart from having been one 35 years ago.
You say that you have tried offering your daughter lots of things (7 things to choose from on her plate). As someone with autism, this sounds completely overwhelming to me. Like a lot of people here, I can eat one thing consistently for months and months. I like the fact that it is familiar and predictable. If you put 7 things on my plate as a child, it probably would have melted my brain, and I wouldn't have eaten any either.
My suggestion (obviously run it past her doctor first), would be to choose one thing which is nice and nutritious, and give it to her every single day, day in and day out. For months if necessary. When it becomes familiar, you may find that she starts accepting it, and trying it. I wouldn't even make a fuss or encourage her too much until that thing on her plate becomes very familiar to her. I know they recommend representing food multiple times to children, for one with autism this is probably ten times more important.
If you can get to the stage where she accepts one thing, then slowly introduce another thing. Slowly, slowly, slowly. I don't think I was as bad as your daughter, but I was a really picky eater as a child. If anything upset me or threw me off my routine, I just wouldn't eat. I was always underweight and sickly. Unfortunately I'm not able to tell you how my parents coped when I was your daughter's age, I can only tell you what I remember.
One thing that helped was that meals were always very predictable. I knew that I would always have X for breakfast and Y for lunch. Dinner in our house was on a schedule, so on Monday we would have meal A, Tuesday it would be meal B, etc. Sometimes I might decide I didn't like dinner B, and I wouldn't eat it, but the schedule was comforting nonetheless. After six months, I might decide I was bored of lunch Y, and suddenly change to something else, which I would then eat every day from then on.
Anyway, you may have tried this option too, but certainly from my perspective, the choice you are giving her may be counterproductive.
I hope this helps a little bit. Good luck with her.
By the way, if it is any comfort, I did get better as I got older, and now, apart from preferring familiar things, I do eat normally and can regularly be persuaded to try new things.