I thought the caravan looting for the hospital was gone now? Have some vague memory of that getting squashed. My personal peeve has always been spoiler thread stitches which feels like a sacrilegious waste.
I also have an aversion to zoning a hospital before i have soap available, but that stems back to an old bug where they would fill everything with thread/cloth and there would be no space for soap when it was eventually made. I believe that bug is, if not squashed, less blatant these days.
Catsplosion wont just happen like that, so dont panic yet. Its only cats that have adopted a dwarf that you cant easily dispose of, and they will only adopt dwarves that have a preference for cats. Its something you might see more as your pop climbs, just keep an eye on the pet screen and on who is being adopted. A few cats around is a good idea since they keep vermin down, ideally you want only 1 female to be adopted though.
Sounds like your fort is running pretty stable, you might want tostart a construction project, expand your mine workings, go explore a cavern. All of these are fun distractions. I would probably sort that hospital first though. Its certainly a good plan if you are going to the caverns, and the logistics of getting a water cistern and wells set up is a valuable learning experience.