Yes, you are allowed to take food into the parks. All bags are searched as you enter the parks.
Water bottles are nice to have and can be refilled at any faucet or drinking fountain.
I usually try to freeze the bottles the night before. Then we drink them as the ice melts. Helps to keep them colder longer. We have cases with straps to keep the water bottles in. I have everyone carry their own bottle. I carry a backpack with snacks or lunch. Also for the camera or camcorder.
For Disney, you will need at least 1 day each to enjoy each of the 4 parks. You will spend most of the time in lines.
Disney has a new feature to help with the wait in lines called "Fast Pass". You choose a ride and then go to a machine near that ride and run your ticket through it. It then gives you your ticket back and another paper to let you know to come back within 2 hours to ride this ride. Now you can go stand in a regular ride line and when done with that ride, run back to the first ride and get in the Fast Pass line.
We have been to all of the Disney parks. I went on a School Field Trip with my DD to the Kennedy Space Center. And we have annual passes to Sea World.
School gets out May 24.
I hope this helps. If I can answer any more questions, just let me know.
Kathy