Backcourt
 

1) A-1's try rebounds off the backboard and is batted towards the division line by A-2. A-3, while airborne from frontcourt, catches the ball and lands in the backcourt.
2) A-1's try rebounds off the backboard and is batted towards the division line by B-1. A-3, while airborne from frontcourt, catches the ball and lands in the backcourt.
3) A-1's try rebounds off the backboard towards the division line. A-3, while airborne from frontcourt, catches the ball and lands in the backcourt.
4) A-1's Throw-in is batted towards the division line by A-2. A-3, while airborne from frontcourt catches the ball and lands in the backcourt.
5) A-1's Throw-in is towards the division line. A-3, while airborne from frontcourt catches the ball and lands in the backcourt.

Which one(s) is/are legal?

#5

Agreed.

And, to be clear, no long switches here. ;)

While I agree with this as the rule is current worded, I think this rule is poorly worded. I feel it would be more appropriate for it to say that a player who's team is not in control of the ball is allowed to catch the ball and land in the backcourt.

It would make it very simple and would eliminate all of those cases about the ball being tipped before being caught on a throwin.

Well... isn't there team control during a throw-in?

Another little twist.

6) A-1's try rebounds off the backboard and is controlled by B-1. B-1 throws the ball towards the division line. A-3, while airborne from frontcourt, catches the ball and lands in the backcourt.

Legal.

What's the twist? this happens reasonably often (several times a year). This shouldn't even be in the discussion for a BC violation, it could actually confuse some.

The twist is likely that many do not know about the exception to the BC rule for the defense intercepting a pass while jumping from the FC, catching, and landing with the ball in the BC.

Yes and no. Team control only exists in the context of fouls for a throw-in. For all other purposes, there is effectively no team control.

Just for clarification, if the ball is in the air during that pass, and A1 jumps from his/her frontcourt, and catches the ball, it's clearly legal.

What if the ball has bounced in the frontcourt, and A1 jumps from his/her frontcourt, and catches the ball between it's bounces, and then A1 lands in the backcourt? (I have a colleague who insists that this would be a backcourt violation.)

Tell your colleague to read NFHS 9-9-3. The ball being in the air or bouncing has nothing to do with it. It's the human. If the defender is airborne when (s)he catches the ball the play you're describing is legal.