Mary,
Yes, and yes, you can bring food and water into the Disney theme parks!
Bringing in a backpack or other bag with some provisions for the day is a great way to keep within your budget. It also helps ensure that everyone has the treats they really want and that they are staying hydrated throughout the day.
Each Disney theme park has a bag check where they will perform a quick inspection. It is a fast process, nothing that will significantly delay your arrival into the magic. You will then find that many of the rides have a space in your ride car to store a backpack while you ride. That is not on every ride, but it is on most attractions where it might be needed.
If you are going to the parks from some resorts, the bag checks can even be at the hotel. This helps alleviate longer lines directly in front of the park. Examples of this include the monorail stations at
Disney's Polynesian Village Resort and
Disney's Grand Floridian Resort & Spa. There is also one on the walk from
Disney's Contemporary Resort to the
Magic Kingdom Park.
BONUS TIP
I don't always want to carry around my backpack, so I will use one of the in-park
lockers to store it while I go on rides. Always found at the entrance to the park after passing through the turnstiles, there are a few locker sizes available. They are keyless and typically will cost you $15 or less for the day. The Magic Kingdom Park and
EPCOT even have a few larger lockers available that are up to 17" x 22" x 26" (43 cm x 55 cm x 66 cm). Prices can change, so check first online for current rates.
Write me back if you have any follow-up questions.
Have a Magical Vacation!
Doug