Not sure about hats on slides. I suspect you can't wear them, you could probably hold them, or just leave them at the entrance.
As to shoes, from a UO representative in response to a trip advisor question - Thank you for your question. You are able to wear water shoes in the pools and rivers like Waturi Beach and TeAwa the Fearless River. However, footwear is not allowed on any of the tube attractions. For more detailed information we do have a Volcano Bay Rider's Guide available on our website. I hope you found this information helpful.
I usually wear flip flops and leave them at the ride entrance (there are racks at most)
I always have a clear hard plastic case for my ticket, room, key, etc around my neck and am sometimes asked to tuck it into my suit. If you plan on doing the trapdoor slides (or body slides? I don't do those) they might no be allowed.
I usually hold my sunglasses on the tube slides. I sometimes can wear them on the water coaster (water sprays in your face on parts of it), sometimes they tell me to take them off.