C.C.
Can you put her in school? My younger daughter (5 years old) is "spirited" (to put it mildly). She always has been. The only thing I have ever found that helps is to challenge her (REALLY challenge her). As such, she has been able to do jigsaw puzzles since she was just over a year old, learned to read when she was 3, could do her big sister's 2nd grade math at 4, and this year at 5 is in 1st grade (bossing all the boys around, I might add)... you get the idea. A child like this is very, very intelligent and needs to have something to keep her mind busy, or she will be forced to create ways to entertain herself. (And some of these ways are guaranteed NOT to amuse mommy! Like the time my little darling filled all my shoes with conditioner. Or the time she decided to dump a box of crayons into the dryer with a load of whites, and turned it on... so charming!) However, once we figured out that we could introduce her to new ideas and let her run with it, she became much calmer in general. For instance once she learned to read, she discovered that she could read books, which is an almost endless source of amusement for her. Once she learned how to add and subtract, we could give her a sheet of math problems and that would keep her busy for a good half hour. She gets the biggest kick out of flash cards. (How long will THAT last? LOL)
With regard to the eating issues, just ignore them. My daughter will have phases where she will go into a huff over food. I used to freak out about it. Now I don't react AT ALL. Put the food in front of her. If she doesn't eat it, oh well. No food until the next meal/snack time. Don't make any commentary, don't feed into her drama. It will pass much faster if you refuse to give her any reaction.
I have no idea if this is "normal" behavior - my older daughter never did it, but I think she has always been a really easy kid so who knows. But I guess if your kid is like this, and my kid is like this, then at least we're not alone! ; ) Just find something that really captures her interest - whether it is school work, music, theater... get her involved in it so she has something to keep that busy brain from thinking up mischief!