When A1 is fouled and will be given free throws, but A1 can't shoot because he/she is injured, hurt, dead, etc., who picks the shooter? I thought it was team B's coach, but I could be wrong.

Team A's coach can choose any player on his bench to shoot the free throws for A1. A1 cannot return until time has come off the clock.

A can "buy" A1 back into the game with a time-out to shoot the free throws, but only if he has not been substituted for at the time of A's time-out. Otherwise A1 may not re-enter until time has come off the clock.

Luke, that's the NBA rule, but is not the case in HS or NCAA

No one picks the shooter. A1's substitute will shoot the FT's.If no sub is available, a teammate on the floor can be designated by either the head coach or captain.

Must be why I thought that, just couldn't remember the rule at the time.

This happened to me in HS. I got knocked out when being fouled. I came out of the game. My replacement made both ends of the one-and-one. After awhile, but what was really only 6 seconds in elapsed time, I went back in and finished the game. That would never happen today because a doctor would not have cleared me. The opposing coach was hopping up and down. [He must have had a scouting report on my free throw shooting]. The rest of the game was a daze.

Also, the player may not re-enter the game in the NBA.