I've seen more rats than I would like. That comes from keeping chickens. I recently got a feeder that seems harder for the rats to access as they were getting most of the food. They are pretty smart creatures really. I don't know how much they are worshipped, but they are part of the Chinese zodiac.
Yes, maybe in China they do - and at least in the zodiac. Elsewhere it seems to be a bit in competition (and symbiosis) with another very successful race of animals which has shitcoins, tupperware and lawnmowers.