I would contact the group organizing the wish trip, as they will likely have some specific advice, such as information about break rooms, for you.
As for the food issue- I would recommend you plan for table service meals if the allergies are complicated - it's hard to really say much not knowing which allergies he has. Generally table service are much better at addressing specific food requirements for you and will have more options available. Have you looked into making any reservations? You would be able to do that now and it may make things much easier for you.
We have had a great time dining in the Magic Kingdom at table service with allergies. We've become big fans of Liberty tree tavern (for lunch, never done the dinner there) The plaza and Tony's. A big thing is to look over the menus and try to guess which food is closest to what he would want. If you want character dining we also liked the Crystal Palace, which has the winnie the pooh characters.
What might be a good place to start is for you to contact special diets (SpecialDiets@disneyworld.com) and see if they have any lists of specialty foods for the specific allergens you are dealing with. They keep lists of specialty foods for gluten, egg, dairy, soy, peanuts and treenuts. (they might have more)
Basically you can get meat, veggies and fruit anywhere. If there are certain toppings, marinades or sauces that are an issue you would need to speak to the chef on site to see what they can do. If his allergies are items that are easy to avoid, you may be able to look over menus and pick quick service locations with options he likes. My son goes place to place and ends up with grilled chicken or fish, plain rice and a steamed vegetable but we rarely eat a meal that is not table service.
I don't know about puree capabilities but special diets may also be able to help you there. I would expect that the quick service locations would not have that option.
Outside of the Magic Kingdom we've found allergy options to be more complicated. We've been sticking to Tusker House at Animal Kingdom, we liked Biergarten at EPCOT (many world showcase places can be riskier with allergies, they seem to understand them there) and we have found Hollywood studios frustrating because we can't eat the quick service there and the table service you can't get near without a reservation made the day the window opens or at a horrible time. It all really depends on what you are avoiding.