Like babies kittens tend to have high energy for short periods of time and then they wear out and need to sleep. They tend to sleep a lot until they are over a year old and their bodies start to slow down on the growth side of things. They also eat a lot when they are young and as they slow down on growth they don't need as much food. In their second year they tend to reduce needed sleep and food intake and their bodies settle down. They are pretty much like people, when they are young they need to grow so they need more food and they need to rebuild so they need more sleep.
As mentioned above Kittens can be sleepy after they play. As for eating mice, my boy Munchie was catching them when he was just a few months old. Even my old lady has caught mice. Mind you my cats are indoors, we had a mouse problem at my previous house.