Allison,
Thanks for your question!
Yes, you absolutely can carry a backpack of your own snacks into the park. That is a great way to keep the family energized, and it can also save you some money along the way. When we go to Walt Disney World most breakfasts consist of each of us with our own granola bar of choice that we bring in with us, and then we purchase a container of fresh sliced fruit from one of the stands in the parks. We share that between the four of us, giving us a healthy, and fresh start to the day.
As for water bottle filling stations, yes, Walt Disney World has several in each park, and are adding more periodically. The old solution was asking a counter service restaurant for a glass of water, which they would gladly provide free of charge. But with the growth of water bottle usage, they clearly felt the need to add more self-serve options.
You will find that there are several of these water stations in each park, and they seem to add them as they design or renovate certain parts of the park. A few have been placed in locations where you really would have to be in line for a specific attraction to access the fountain, but you should still be able to find an available one in each park regardless. The park maps do not currently reflect these locations, so you will want to ask a cast member where to find the nearest accessible fountain.
The resort hotels also are adding these as well, though I have not seen one in every resort, so I cannot promise anything. But staff at the resort's counter service restaurant can always help you out. By the way, the water is filtered, so that is a plus.
BONUS TIPI am not crazy about carrying around a bag during a day at the parks, so I will often use one of the
lockers that you can rent in each of the four Disney theme parks,
Disney Springs, and both
water parks. They are all typically located at the front of the park, and I can stash my backpack there until I need something later in the day.
Have a Magical Vacation!
Doug