Damage is whatever a task pays. 100 HP is one gold of work.
Companions and garments aren't split — you each get one, so neither of you is racing the other to the drop.
Both go into the shared pool, so any pet can wear them. Leave the subject blank and the monster's own name is used. Leave the prefix blank and one is rolled at random. A joining word is optional — it just adds to the shared list.
Meow Bucks and XP don't touch the weekly task-rate budget. XP also pays out double in Meow Bucks on its own, on top of whatever's set here.
Every kill, permanently — fighting a monster again (or deleting it) never removes its past battles from here.