I'm not sure how deep the deepest part is, but I can definitely stand up in it quite easily and not even come close to my head being under water! lol I'm 5'4", by the way. The deepest end is the furthest end away from the beach area. It's right where the stream enters the pool.
This leads me to your next question! For the first time I ever, I took the plunge (literally! LOL) and went down the slide this on this trip! It was a lot of fun and immediately upon landing in the water I was able to put my feet down and stand up. I'd guess it was probably 4' - 4 1.2' of water. However, the water is rushing past you rather quickly at that point, so if a child is shorter, or not a strong swimmer, you might want to be at the bottom of the slide to catch them.

I saw a lot of parents do this. The lifeguards at WDW all seem top-notch and you can see them concentrating on their work, never taking their eyes off the water, while they're on duty. Of course, nothing replaces a parent's attention, when young children are in the water!
I like rum and can't stand tequila, so I can't help you with that, but I'm sure the bartenders will be able to mix up something that you'd like. lol
I hope you have a great time at the Polynesian!!