Just as a heads up, if you are ordering something that is normal an adult's item and trying to get a child's size, verify that they can do a child size and charge you a child's price so there aren't any surprises.
We have fairly bad luck with CS, but among the strange issues have been places offering to make a small order of something for our 4 year old, and then it gets rung up for $10 with no drink or dessert.
I would go take a look on allears to check out menus for places you want to go in advance. Some people have had luck with CS locations going and getting food from other locations for them, but our experience has been if they don't have it we have been told to go elsewhere as often as we have had them serve us. The only non-resort counter service who have served my son have been Columbia Harbor house, sunshine seasons and backlot express. To be fair, we have only been turned away from Pinocchio village haus, studio catering co, starring rolls, and columbia harbor house (different manager that day) so we have not tried a lot. It only takes one turn away for us to start asking TS for walk-ins now.
If you are staying on-site, I recommend contacting special diets because you have 4 allergies and 2 are not specifically on their checklist. That way if you plan to eat at your resort they will know to get in edible items for you. We have found eating at our resort to be much easier when figuring out CS.