are water bottles allowed

Yes! You can bring them in a small cooler, as well as your own food. Check the Disney website FAQ before you go, because they are always changing the rules. It's best to stay up to date.

Yes

Yes to the water

If they allow to enter, but what they recommend is to take small thermos with wide mouth to load water in the drinking fountains and ice in the stalls selling drinks. Ice is free, you have to ask for it. Enjoy the Disney parks