For the cat door, it might help to aim the camera so the cat walks across the frame rather than straight away from it, since the motion sensor on the battery cams reacts much faster to side to side movement. As far as I know you can’t set different clip lengths per event type, but in the camera’s Event Recording settings you can pick which smart detections trigger a recording, so unchecking Person should stop those clips. It’s also worth checking the cooldown setting there, since a long cooldown would explain missing the cat coming back in.