Substitutes - When can they enter?
 

A1 is lined up to shoot 2 free throws. B1 calls a time-out. After the first horn, A6 attempts to substitute. When can A6 enter the game?

Team B has a throw-in. B1 calls a time-out. After the first horn, A6 attempts to substitute. B1 violates on the throw-in. When can A6 enter the game?

After the first free throw.

After the violation.

Let's Play ...
 

A6 has reported and is waiting at the table to substitute for A1. B1 fouls A2 in the act of shooting an unsuccessful try. After foul is reported, but before any free throws are attempted, Team A requests and is granted a sixty second timeout. When can A6 legally enter the game?

A6 can legally enter when Team A returns to the floor.

These sound like test questions.

Wouldn't A6 now have to wait since the first horn has sounded?

BktBallRef's answer of "A6 can legally enter when Team A returns to the floor", was responding to BillyMac's question.

The A's Have It ...
 

3-3-1: A substitute who desires to enter shall report to the scorer, giving
his/her number.
a. Between quarters, at halftime and during a time-out, the substitute must
report or be in position to report to the scorer, prior to the warning signal
which is sounded 15 seconds before the end of the intermission or the
time-out.
c. During multiple free throws resulting from personal fouls, substitutions
may be made only before the final attempt in the sequence and after the
final attempt has been converted.

Common sense tells me BktBallRef is correct. The rules also tell me BktBallRef is correct if we assume that Article A trumps Article C.

The question to be asked when considering A vs. C is whether you can be "during a FT" when you are in a timeout.

The purpose of C is/was to speed up the game a little by not allowing subs at a time that would be of no additional value over making them wait until before the last shot. Allowing a sub in the middle of the timeout has no impact on the flow of the game.