There is no evidence that chytrid is carried by the air. I recommend having them physically apart, such as in different rooms, simply to put more of a barrier between the tanks, so less water is exchanged. There's more effort to go from one tank to the other, and maybe there will be more of a reminder to properly clean your hands and arms beforehand. Also, having them apart makes a nice set-up for a schedule where you play in all your other tanks one day, and maintain the chytrid tank, farther away, and therefore not so convenient while cleaning the rest of the tanks, another day altogether. It's less temptation to "fix this one last thing" and plunge chytrid-water arms into a chytrid free tank, or splash, or mix hoses and pitchers, that kind of thing.

I don't know about chytrid in tap water. I'd say it's impossible because of the treatment process, but I don't know the details of the treatment process to be 100% sure.