Yes for both, make sure when you're leaving to ask if you need your hand stamped. You can take food into Universal, they allow "small snacks that don't require heating." I've heard Disney allows food too, as long as it's similar. Their lawyers are probably terrified of killing someone with food allergies if they can't bring in non-peanut contaminated chow or whatever.
Leaving in the middle of the day is usually a good idea just for the break, but eating in the parks isn't too bad. Universal has Citywalk right outside the gate, they have a Burger King, Moe's and other okay choices to save money. Your best bet is to eat a big breakfast, they have cheap buffets along the main roads like I-drive. If you do eat in the parks, you can save by looking at menus ahead of time, instead of bumbling around.