Colonizing: definitely.
Warlord: 100%, if that’s what you’re into.
20 cats: only the one, I believe; and a dog, if they can get along. But there are mods.
Perpetually horny: oh, yeah. Practically the name of the game. Unless you become impotent, of course, or live in Byzantium and get on your liege’s bad side.
Getting your house on fire: metaphorically…? Sure, constantly. Literally? I don’t think there’s an event for that, but there’s that one with the basement full of manure…