To feed the cat, you ned to win games in Norstein Bekkler's Tent of Horrors. Win the games once to get the prize, and with the same lead character, win the game again to get cat food. it'll go straight into the bowl in Crono's room. You can also breed cats this way. First, win the 80 point game to get a second cat. Then win cat food and keep doing it regularly throughout the game. The most you can have is 11 cats, the last of which'll be purple like Alfador.