a- Was this a timeout situation?

b- Shouldn't that read "may not enter the game until the ball becomes live."

No. The requirement is that the clock runs. The ball can be live without the clock having run.

True, but if you have free throws following the timeout (but before the clock runs), you'd let the player in.

Or, if another timeout was called and the player reported before the warning horn of that timeout, you'd let the player in.

The requirement for the clock to run only applies to a player who has been substituted for (sorry for the dangling preposition there).

a - yes, per the OP

b - it really doesn't even have to go live. "until the next opportunity for a substitute."

chseagle-yeah this was the only gym I've ever been in where it exists.Other schools around here have a multiple gym system!