food is allowed in - but there aren't any Picnic type places - there are a few tables in a few areas in MK that you could sit at IF there are any open-
and a few tables in other parks but it isn't easy finding a free spot
soft sided small coolers like what you can fit a 6 pack of coke cans in will fit in a locker-
I have NEVER had any issues taking in food these days-years ago that wasn't the case
We take munchies in all the time- not real food but my special pretzels and fruit snacks -trail mix etc..
but I have been with people who bring in sammies, rent a locker and sit on the sidewalk and eat.
I have NEVER had any issues with speaking to a chef about my or DD allergies with food- I have NOT eaten in Mexico or Morocco- I have eaten in Italy and they had gluten free pasta for me but I had to call a few days in advance -I have had issues with them maybe only offering grilled chicken and rice and I can eat that at Home

Crystal place chef was NOT helpful last time- I spoke to a supervisor and all was taken care of ASAP
Don't be afraid to speak up and inform the wait staff and others as to your allergy needs.
I can find food at rain forest cafe but it isnt much - like a burger minus the bun and a salad- and I have to FIRMLY tell them if you cross contact my food I will become very ill and I will own this company
(Disney likes the phrase cross contact NOT cross contamination)
They do have divvies and the gluten- dairy- nut free brownies which are soo yummy

I think with the special diets team sending you info in advance for counter services it will be helpful and as far as table services go- call in advance and speak to someone on the special diets team. Disney is wonderful for us.