My own memory of New York is that if noticed an absence of roaches in your apartment, that meant you had mice, and the mice were eating the roaches. I told a friend that (she had happily commented about not having roaches) and she looked rather alarmed. I should have kept quiet.
A friend's parents used to have a maine-coon-esque cat who once brought home a lamb it had discovered in a nearby field. Would have had to get this thing over at least two fences but somehow managed.
Our cats have discovered that dead mice aren't any fun to play with, so they'll go to great lengths not to kill them. They'll pounce and stun them for a bit, then the mouse recovers and tries to scurry off - and the cycle repeats. Eventually the mouse finds a safe haven where a cat can't get to it.
No, just butcher all but one of the female cats to make *cat meat roasts*, and stick the spare in a cage. (Keep the males for vermin control.) See also [0].