A: Yes, the Cute Fuzzy Alien (CFA) absolutely counts towards the Keeper Limit. The player whose turn is ending can decide whether to pass the creature and then comply with the Keeper limit, or comply with the Keeper limit and then pass the fuzzy creature. The next player may decide to do it differently if they want.
So, when the CFA is discarded, it goes onto the top of the draw pile instead of the discard pile. This has the possibility of causing some loopy-type action, but it’s not that difficult to disrupt unless you have really stubborn players.