A neutered cat will stay trim with a normal, balanced diet. Cats are perhaps the most curious creatures on earth. They can get themselves into a whole lot of trouble because of their curious nature. The cat is an explorer and is constantly on the hunt. Part of the reason for their curiosity is that they are always looking for food.
Some hunts don' t end up all that successful.
It is probably a happy dream about chasing and catching mice. Just like humans cats alternate phases of deep and light sleep. Sometimes they even vocalize and snore. Even though they seem dead to the world while sleeping, don't assume they are, they can spring to life in an instant. When cats rub up aginst you, other cats, the wall, the couch or just about anything she actually is depositing her scent.