I am trying to get this all straight... 1. I am allowed to bring a cooler strictly with ICE and SEALED water bottles, yes? 2. Are there places to lock up our stuff if we bring in our phones, wallets, towels, etc? 3. Is there plenty of shaded areas?

Yes plenty of shaded areas yes with the cooler and water and they have 3 sizes of lockers you just have to pay for a locker and we left our towels out to save our chairs a lot of people leave there towels and bags with like sun block and their clothes in it out

The shaded areas are tricky also because of the location of the sun. For example a shaded area at 11 am may not be shaded at 3pm.

You got it on all 3. Although if you want to get a shaded area you better get there earlier rather than later.