There are loads of formulas that we use in the industry, but everything is open for interpretation, especially when dealing with a pack of hungry kids.
A goof rule of thumb we use for banquet events. these are based on a per person count:
So, for 20 people, it would be:
6x20=120oz, divided by 16(oz to the lb)= 7.875 LBs of protein. . . round up, 8lb
4x20=80oz, /16=5lb Starch
4x20=80oz, /16=5lb Veg
1.5ozx20=30oz=3.75 cups of sauce/topping
Again, these amounts are conservative, and your mileage may vary, but it is a good tool to know so you aren't over/under producing, and there are factors to take into effect, like hungry kids. You know your group, so anticipate the needs accordingly.
Baking/mixing batter in bulk, is typically frowned upon, as not all ingredients translate well to large batches. We have always done triple batches of standard recipes at the most. It allows better control, as baking is chemistry/formulas, and not as forgiving as just cooking.
Timing of an even just boils down to practice and common sense. Typically, if doing a whole bird, or joint, or roast, the veg can all be done in the time it takes to rest the meat. the starch can be made ahead typically, and held, as can sauces. Having the main, HOT, and the veg(still al dente, and colorful) done right are really the major timing issues. Just allow your self time to adjust the small things. The bigger things, once they are gong/done, you have very little control over.
For bulk hot dogs, cooking and holding, here is a great "Parking lot Sous Vide" we have done for tailgating, and picnics: get a cheapo 7-11 styro cooler, wash it/rinse it, and fill with water JUST below the boil. Place in hot dogs, put a lid on it, and done. They will stay hot for hours. You aren't worried about specific temps(med rare, med well, etc)so it's nothing to worry about.
So you don't think I am off my rocker:
Cook Your Meat in a Beer Cooler: The World's Best (and Cheapest) Sous-Vide Hack | Serious Eats
Most other picnic food is made for high mileage, so it shouldn't be that bad. make stuff the night before, have veg(onions, tomatoes, pickles, lettuce)all sliced,and stored in bags between layers of damp towels.
I am sure others will chime in, but just remember: It's lunch and dinner, not life and death. It's nothing to get stressed out about,and preparation is key. Stay a day ahead of the game, so that the day of, you have little to worry about, and can handle the small hiccups more easily.