You won't find a list of ingredients anywhere on line because Disney refuses to publish it since suppliers change constantly and even from one meal to the next the chef might use a different batch of something.
You will NOT have any trouble eating well at any location. My list of safe foods is shorter than the foods i need to avoid and I still eat like royalty! You will do best at sit-down locations because you can ask to speak to the chef and they will help you figure out what's safe to eat, rarely are my meals even something that's on the menu. You should note it on your reservations and click the "other" box for allergies and when you arrive remind them that you have allergies and that you need to speak to the chef because you're not "top 8" covered. You will be able to eat at buffets even -- if foods aren't safe they will bring it to you directly from the kitchen.
At counter service locations and even the little carts that sell popcorn and other treats you can ask to see the ingredient binder and they will have the lists of every.single.thing they sell. When you go to order at a CS look for a CM who is wandering around, usually carrying a clip-board or if you don't see anyone like that mention allergies when you get to the till and ask to speak to the Allergy Trained Manager. It will take longer to get your food prepared but I haven't ever needed to go hungry -- in fact, for me it's all about the food!!