Injured Player: When Do You Stop Play?
 

A1 drives and lands hard after his shot. He's on the ground while B is taking the ball up the floor. Its not a fastbreak but they are quickly in their set offense and getting ready to start the play.

A1 is still on the ground under his own basket.

What are the determining factors when deciding to stop play or not? Does B have to be taking the ball to the rim in order to let them play on?

Quoting directly from the rule book:

When a player is injured, the official may suspend play after the ball is dead or is in control of the injured player's team or when the opponents complete a play. A play is comleted when a team loses control (including throwing for a goal) or withholds the ball from play by ceasing to attempt to score or advance the ball to a scoring position. When necessary to protect an injured player, the official may immediately suspend play.

This is the part of the rule that is open to interpretation. In my scenario, if the injured player is down under his basket (and lets assume there is no bone sticking out or anything like that and that he is conscious), what do you do? Keep the play going until B loses team control?

As the new trail, you stay with the player. That tells everyone you are aware of the player and you will stop play at the appropriate time.

When the opponent pulls up and is no longer attacking the basket, you kill the play.

Are they "attacking the basket" if they're running their set offense?

If they set up their offense. I let them end it. How ever, I have had teams who simply stop playing offense. Then I stop play, it's there choice. But unless the player is badly injured or as it says, needs protecting, I let them play things out...
If they take a shot, grabs the offensive rebound, and sets up again I will call it dead though (the play has been completed, so call it dead, no need to start a new offensive set).

Had it last night where a player sprained his ankle with 8 seconds left and the winning team got the ball, came down floor and the game ended. Players and coaches were both ticked we didn't stop the game. A few seconds later the kid gets up and walks off.

No, they aren't. If they're dribbling the ball out front, passing the ball around the perimeter, etc. I kill it.

Had 2 situations like this today. First one, B1 is down near division line in backcourt. A1 is dribbling paralell to division line near the circle. I killed the clock. 2nd one, B2 is down near the foul line. A1 is contested by B3 near the division line in the backcourt. I killed it. I would rather err on the side of caution although Coach A claimed that they had a fast break going. I have never seen a 5 on 4 fast break with the ball closely contested in the backcourt near the division line and the other 7 players in the forecourt. Then Coach A says that the opponents are going down on purpose to stop play.