So, I'll ask this question and hope that most of you don't chastise me too badly for not knowing this.
What's the call if A1 with the basketball passes to a teammate but retrieves the pass himself? Does it matter if you are on the move or stopped with or w/o your dribble left?
Any words of wisdom on this one would be appreciated. Thanks.

I would call travel in this situation. What happens is that when a1 passes, it is in his player control, and while he is moving to retrieve, he is moving his pivot foot in order to do so. Whether he has his dribble left is irrelavent. It is different on a shot because loss of player control occurs on a try. In this situation, a1 can legally retrieve what many fans and coaches believe is "catching your own pass" without penalty.

Need more info on this Queston. If he hasn't started his dribble, and the ball hits the floor when he passes, then he can retrieve the ball.

Federation rules: Rule 9, Section 5

"A player shall not dribble a second time after his/her first dribble has ended, unless it is after he/she has lost control because of:
Art. 1 ... A try for a field goal.
Art. 2 ... A bat by an opponent.
Art. 3 ... A pass or fumble which has then been touched, or been touched by, another player.

So, we know that if A1 looses their dribble, passes a ball which touches another player, then they can dribble again. This also means that if A1 looses their dribble, passes to A2 who has their back turned, the ball hits A2 on the back, then A1 can pick up the ball and start a new dribble ie. the touch does not have to be intentional.

My outstanding question:

If A1 has their dribble and attempts a pass to A2. A2 moves out of the way (inadvertently!). The ball hits the floor (obviously!) and does not touch A2. Can A1 recover the ball and still have their dribble? ie. does the bounce resulting from a pass count as the dribble (since it did not touch any other player?)

My guess is "yes" since the pass to A2 was not intended as a dribble, so A1 should still have a dribble.

My call would be no call. A has not dribbled, so he can recover the errant pass and resume his dribble as long as he doesn't catch the ball and resume dribbling.

I agree with Tom and Todd (as usual).
If A1 already used up the dribble it would be either a double dribble (started and restarted dribble) or a walk as pivot foot had be moved to regain possesion).
If ball was just caught (triple threat position), you can think of it as one long dribble. It be one of those plays that look ugly, but legal.

I agree, Tom. A dribble can be started in several different ways, and throwing the ball (whether on a pass or not) is one of those ways----as long as the ball hits the floor before A1 touches it and he doesn't CATCH it, as you said.