1) Not. too likely. But it's not unheard of. Generally if they're in those areas, they're there to commit some petty theft, not get violent with each other.

2) Given Celestials tend to be highly protected individuals, they are unlikely to try and start shit, less the Tamamo Clan come down on their heads and disappear them all. They're upset at things, but most of them are smart enough to know not to pick a fight with people they can't hope to touch.