1) Turn off the tap. (Do we say turn off or something else? Also what do we say to turn it on?)
Yes - you turn on and turn off a tap.
2) Who left the tap running? (I mean the tap was not [STRIKE]closed[/STRIKE] turned off.)
This question is correct.
But, now I think of it, if you leave it on, that's not separable: 'leave the tap on' :up: but 'leave on the tap' :cross: - interesting. ;-)
b