When does the ball become dead?
 

I understand if a offensive player releases the ball and is then called for a player control the shot does not count as the ball is dead right away. If A1 shoots and while the ball is in the air, A2 pushes B2 while trying to get position for rebounding, does the ball become dead or would the basket count if it goes in. There is no player or team control on a shot, so I thought the basket would count.

Your instincts are correct.

Instincts are correct for Fed.

Under NCAAM, the shot would count.

I clarify because the OP didn't specify any teams that were playing or what rule set is being used.

Why did you clarify your clarification? It was obvious, and it's sad that you had to do that. ;)

NHref007 - welcome!

Assuming you are dealing with NFHS rules, 6-7-4 says the ball is dead when there is a player-control or team control foul. Since you said there is no team control during a shot, your instincts are correct that this doesn't make the ball dead. So, then we go to 6-7-7 that says the ball becomes dead when a foul occurs. However, there is the exception at the end of that section that says the ball does not become dead until after a try or tap ends, or the airborne shooter returns to the floor. (With other caveats as to whether time expires during that period, etc.)

So, your instincts are correct, and now you know where to find the backup in the rules.

I Hope That You Didn't Expect A Simple Answer ...
 

The ball becomes dead, or remains dead, when:
ART. 1 . . . A goal, as in 5-1, is made.
ART. 2 . . . It is apparent the free throw will not be successful on a:
a. Free throw which is to be followed by another free throw.
b. Free throw which is to be followed by a throw-in.
ART. 3 . . . A held ball occurs, or the ball lodges between the backboard and
ring or comes to rest on the flange.
ART. 4 . . . A player-control or team-control foul occurs.
ART. 5 . . . An official’s whistle is blown (see exceptions a and b below).
ART. 6 . . . Time expires for a quarter or extra period (see exception a below).
ART. 7 . . . A foul, other than player- or team-control, occurs (see exceptions
a, b and c below).
ART. 8 . . . A free-throw violation by the throwing team, as in 9-1, occurs.
ART. 9 . . . A violation, as in 9-2 through 13, occurs (see exception d below).
EXCEPTION: The ball does not become dead until the try or tap ends, or until the airborne shooter returns to the floor, when:
a. Article 5, 6, or 7 occurs while a try or tap for a field goal is in flight.
b. Article 5 or 7 occurs while a try for a free throw is in flight.
c. Article 7 occurs by any opponent of a player who has started a try or tap for goal (is in the act of shooting) before the foul occurred, provided time did not expire before the ball was in flight. The trying motion must be continuous and begins after the ball comes to rest in the player’s hand(s) on a try or touches the hand(s) on a tap, and is completed when the ball is clearly in flight. The trying motion may include arm, mfoot or body movements used by the player when throwing the ball at his/her basket.
d. Article 9 as in 9-3-3 or 9-13-1, occurs by an opponent.
NOTE: If A1's try or tap is legally touched in flight, the goal counts if made, if the horn sounds before or after the legal touching. If the touching is interference or goaltending by A, no points are scored. If B violates, the points are awarded – either two or three depending on whether it was a two or three-point try or tap.

Lightning round
 

Wow, Billy, that was quick.

There's no way he typed that out, either; eh Billy? ;)

Not so fast!
 

Well, that might explain the delay.

I think he dipped his fingers in helium before typing.

Manual Typewriters, Typing In Beat To A Vinyl Record Playing ...
 

Miss Dench, my junior high school typing teacher, would be proud of me.

What if the foul by B2 on A2 happens after:

the shot is released by A1
the horn sounds
the shooter returns to the floor??

If I'm reading correctly the ball becomes dead in the exception listing when the shooter returns to the floor.

Is the foul on B2 ignored unless it is flagrant or intentional?

The ball does not become dead until it is made or is missed. Because the horn sounded before the foul by B2, it is ignored unless intentional or flagrant.

If I am incorrect I'm sure multiple people will correct me.

For clarification, the 3 items I listed were the order that they all happened.

Explain to me what the part of the exception that says "or if the shooter returns to the floor" means and where it would come into play.

I realize that basket counts in the play I described. I'm just not sure if the foul by B2 is called.

Oops, guess I misunderstood. I fixed my earlier post to answer your question.