Are there water filling stations where I can refill my water bottle?

Yes. By the entrance.

There is 1 water fountain by the front gate. We bring bottles to refill

I didn't see one, but I brought a prefilled Nalgene and it lasted me all day.

No, we were looking for them as well.

I've never seen one. They want you to buy their drinks.

Not that I know of...

I dont remember one.

I honestly don't know sorry