Correctable Error/Live Ball

[Spence]

A1 is fouled. Table signals bonus. First FT is missed. A2 rebounds and Team A eventually scores on this possession. When the basket is made the table blows the horn and says it should have been 2 shots.

Assuming it's within the acceptable time to correct the error am I correct that the basket counts, A1 goes back to the line with the lane cleared, and then the ball goes OOB to B?

Secondly, one of the ways a ball becomes live is to "be available" to the thrower for a throw-in. In my scenario above at what point are we saying it "became available" in order to determine if it's still within the limits of correcting the error?

If B1 catches it out of the net and then is on his/her way to OOB in order to throw it in is that now live?

It seems like the window is so small for the ball to be dead that it's almost impossible to correct the error in this type of scenario.

Thoughts?