Yes, you can your own cooler
Yes you can bring cooler bags!!.
Yes
You can take anything you want to the park. However, to go to the attractions, you must leave things in the closet ($ 15 dollars per hour) or if you do not take much, next to each attraction there are mini (open) closets for you to leave your sandal. Give to leave another bullshit..but the space is very small.
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