ball over backboard
 

is it a violation if a shot hits the rim and goes over the backboard but does not touch any support?

Under NFHS and NCAA rules, it is always a violation for the ball to pass over the backboard period. Thrown, deflected, off the rim, it doesn't matter. Passing over the backboard=violation. Of course, this is assuming the ball passes over a rectangular backboard. If it is a fan shaped backboard, then this does not apply.

From The Files Of The Mythbusters ...
 

The front, top, sides, and bottom of the backboard are all in play. The ball cannot legally pass over a rectangular backboard from either direction. The back of a backboard is out of bounds as well as the supporting structures.