Can you bring water

Yes ,they will always allow water ,and give you refills ,I always bring their refillable container that I've had for 15 years and they still fill it for the discount price ,and my wife fills hers with ice water for free

You can only bring water in a receptacle.....not like a case ...this receptacle can be used to fill at the fountain.

Yes

You can bring water bottles, and ice and water are provided free of charge at most food locations.

If you can take water and filter inside the park, the ice and water are free