1) Player A1 attempt a shot but miss evrything and goes and catch his/her airball and continued to dribble or shoot again legal or not?
I say its legal but my friend here say NO so can u give me the right answer for him?

2) Player A1 dribbling down the court and decide to pass the ball to A2 but see that his /her pass is going to be intercepted decide to hold back the pass but it slip out, so can player A1 go and retrieved the ball after he/she pass it off and decide to pass it again.

1) Legal in NFHS and NCAA rules. Illegal in the NBA.

2)Judgement call. If you rule the attempt to pass a fumble, the player can go and get it. They can then pass, shoot or hold the ball but they can't dribble again. If you rule that the attempt is actually a pass, then the player can't legally go get the ball. It would be a violation as soon as it's touched.

1)as long as it's a legitimate shot attempt it's legal
2)it's a judgemnt and a tough call to make sometimes. usually when a player is dribbling and then attempts to make a pass he establishes control of the ball momentarily. if he does what you describe after controlling the ball I have a violation because you can't pass to yourself.

RULING: You owe Tony five bucks.