Substitution for injuried player and reentry

[All_Heart]

B1 fouls A1 hard in the act of shooting. Team A's coach is beckoned onto the floor to check on his player. A1 eventually gets up, dusts himself off and walks to the bench. A6 replaces A1 and goes to the line for 2 free throws. A6 makes the 1st free throw. Team A calls a time out to discuss their upcoming defense. (a) After the warning horn A1 reports to the scorer's table for substitution; or (b) After A6 receives the ball for the 2nd free throw A1 reports to the scorer's table.

(a) Because a timeout was called for Team A and A1 is ready to play by the end of the time-out, is A1 required to go back in for A6 or is it optional?

(b) A1 is allowed to substitute after A6's made free throw because of the time-out, correct? Or is A1 not allowed to reenter because he was not ready to play by the end of the time-out?