1) Carnival's food is very good. Most of my cruises have been on Carnival and Royal Caribbean with a couple on NCL. Of the three, as for the main dining, Carnival is the best.
2) Carnival's pools are ever bit as large as the other cruise ships. The Carnival Liberty has three pools. Here are some photos of the pools on the Carnival Glory (a sister ship to the Carnival Liberty - so the pools and water slide will look the same) ...
This is the middle pool ...
This is the aft pool ...
The top over the aft pool can be closed. This is also the aft pool ...
And this is the forward most pool and the water slide ...
3) If the ship is full, then yes, the Carnival ships can feel crowded.
4) There will likely be two productions shows in the main theater and other shows that are family friendly. Then late at night there will additional entertainment that is more adult oriented.
This isn't the best picture (I need a more powerful flash or a better camera which I now have). However, it is the main show lounge on the Carnival Glory (a sister ship to the Carnival Liberty) ...
