Howdy and welcome to the Forum. Great that you start with the important questions!
I don't know of any rules and I'm definitely not the one to make them up. I've seen people with toys in the pools before. As you may know we're going on a new ship. Judging from the deck plan it looks like we have more pool area than we used to but we also have more people. At some times the pools can get crowded, so you may not always be able to fit a whole beer pong game in the pool, at least not without interruptions.
The main pool(s) on pool deck gets decked over for concerts. There is only pool access during daytime (usually they keep the jacuzzis open all night). There are more people around the pools later in the afternoon. When we're in port obviously a lot of peeps leave the boat. This may give you some hints when you are likely to be get the most pool space.