I am not sure. I googled it with no real answer. Most places want you to spend money on expensive plastic bottled water. I refuse
I think they sometimes allow UNOPENED water bottles. It can also change between events, you are best to check with them directly.
In my experience, they don't allow outside food or drink.
Typically yes, for children like sippy cups etc. They normally have no problem with a bottle of water and many people bring drinks into the venue through bags, purses etc.
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