(That's good because the couch belongs to Pippi now. She lounges on it when it gets good sun during the day.) Pippi's pattern, once she figures out what April's is, is to be ready for breakfast when breakfast is served, and then entertains herself while April is working. There isn't terribly much for a perfectly normal cat to do just yet. She spends a decent amount of time poking around inside the pirate ship and using it to sharpen her nails (sadly there's no rigging for her to climb), a decent amount of time lounging in the sun, and a decent amount of time exploring the house looking for pests. Despite the cat doors, she doesn't spend much time outside, as far as April can tell.
She shows her new roommate great respect and affection -- rubbing up against her shins, purring about the food and her touches, and doing her best to cadge as much lap time as she can (which is much less than she'd like). And she doesn't make any messes whatsoever, going in the litter box whenever she needs to, if she's not going outside. In fact, with the frequency of how often she goes outside as opposed to in the litter box, April will probably have to change it less often.
Pippi, of course, does her best to ask for whatever food April is eating when it would befit her to have some (less often than she'd like), and helps out with April's video games as best she can, depending on the game.