In the entire place, you are only over your head in water very very few times. As pp said, the dolphin encounter you are in waist deep water the entire time......IF you want to swim with the dolphin you can do shallow or deep water...just do the shallow swim.
In the sting ray pool, the water is not deep, not anywhere I went.
In the lazy river, you get a noodle and float on it. Most of the time you can stand up and your knees sometimes hit bottom when you are floating and a few times you go over deepwater but it isn't for very long and as I stated you have a noodle to relax on.
When we went the new section wasn't open so not sure about that.
You can wear a life vest if you want but I think you will find that you are very comfortable in all the water areas.
It is an amazing place and you will have a blast!!! Do you have time to take a swimming lesson at your local YMCA or something? That is what I did with my then 6 year old...he swam all the previous summer, then I kept him in swim lesson up until a week before we left. So he got a lot more comfortable in the water and swam like a fish the entire time.