<---- Raises hand. Oooh, oooh, I can help. We always stay off site and almost never eat in WDW restaurants. It's not a food allergy thing for us. It's a combination of budget and that DW and I are into health and nutrition and WDW wouldn't be able to support that. We bring all of our food in, including drinks. We're a family of 5, so if we're going to be in the parks for dinner, you can imagine how large our bag that we bring in is. It's massive. It's a soft sided cooler bag.
I can't help a ton with the allergy aspect of it, that's something best left for you to decide how to avoid. The utensils in all the places we have stayed at are always quite clean. Or we'll just get plastic utensils from the QS restaurants and use those.
As for what we cook, it's easy. People think "cooking" on vacation is work, etc...we don't think it is. Crock pot is definitely good. We'll cook 8lbs of boneless skinless chicken in it. Or just put that same amount of chicken in the oven and bake it. It cooks while we're showering, relaxing, hanging out at home. No real work involved. For the kids...we still have them eat healthy but not quite to the same standards when on vacation...if they don't eat the meat we cook, we'll do things like hot pockets or chicken nuggets. Sides will be things like frozen veggies microwaved and put into soup size Thermoses, or some pasta, or cold veggies such as baby carrots. We use a lot of Tupperware and/or Thermoses. Pizza roll ups are a great idea. If you can't have cheese, then just add some store bought pizza sauce, bake it in the oven and you're good to go. Wrap it in aluminum foil or something like that.
No need to leave it in your van, bring it in the park with you. We have a small umbrella stroller that we use to carry our bag. It fits right in the seat, it's perfect. We'll often just leave it in stroller parking somewhere while we go do our thing. When we're ready to eat, we come back for it and eat (we usually park it somewhere near where we know we'll eat).
