Wrong Way! Wrong Goal?
 

At the start of the second half, the teams play in the wrong direction. None of the officials, players, or coaches recognize the problem. After a couple of minutes elapse and teams make a couple of goals, somebody informs the players on Team A that they are going the wrong way. A1, who is near the goal that should be have been hers had the teams played the correct direction, tosses that ball into that basket. The officials now stop play.

Rule 4-5-4 implies that the last goal scored by A1 should be counted for team B. Does that sound correct?

Second, if an official hears the person inform team A players they are going the wrong way, should he/she stop the game to prevent A1 from throwing the ball into the "wrong goal"? Or, should the official allow the player to finish the play before stopping the game?

Yes, yes, no.

If it were me I would count everything that happened up to the point that the error was discovered and we stopped play at the next dead ball.
Then just switch them around the right way and keep going.

I'm not counting the goal for the other team if someone yells it out in the middle of a play.

Dead ball...inform both teams...switch sides...play on.

Dead Ball?
 

Why does someone yelling it out make it a dead ball? :D

The rule states ...when discovered, all points scored, fouls committed, and time consumed shall count as if each team had gone the proper direction. The official discovered the error when he stopped play and after the goal was scored. IMO the goal counts.

However, if the official recognized the error and was in the process of stopping play before the goal was scoredthe goal does not count.

IMO, the official should stop the play as soon as he knows the teams are going the wrong way. However, if a player had a wide-open opportunity to score at his basket, I would hold my whistle until after the play. I can't see any valid reason to withhold the whistle in the OP and allow a player to score at the opponent's goal.

Bob J is right.

Thank you!