I used an umbrella last year on one of gully washer rains, otherwise I just use a poncho or rain jacket. With an umbrella the problem is holding your food in one hand the umbrella in another now how do you eat your food? I'm just not that talented.
In some, if not most, cases they do actually cook it right there to order. You might could ask for a sauce not be put on but nope you aren't going to have much luck getting anything modified. They punch the order into the computer, you had your receipt to a person who then tells the cooks/servers what you want. I'm pretty sure there are no options on the computers for substitutes. The best you can do is ask before you order if there are any onions or garlic in the item. He is going to be o.k. with the desserts obviously but I'm thinking most of the booths are going to have one or the other ingredient in their dishes. Is it even possible to make Italian food without either?