is there a way to catch the cat? also, how do I get to the roof for the neighbor? I don't see any time to do so
If you are playing the self-sacrifice ending then there is no way to catch the cat.
As for the neighbor, you can do his side quests whenever you are walking up from the first floor to the fifth up to Austin’s apartment. During the time slots where you can search for Austin/go to work/etc, you can go to the apartment and do the stuff for him then, or you can stop by any time after competing Austin’s request for the day — getting groceries or going to the butcher’s for example.