That's just public address announcing. As long as he's not doing commentary, nothing wrong with it.

No written rule but that definitely crosses the line IMO.

Unless the scoreboard clock had malfunctioned, why would it be necessary?

Last season, JC game, we had a clock malfunction at halftime and were unable to properly use the shot clock thereafter. I was charged with the responsibility for the remainder of the game of holding a stopwatch and announcing, 25, 15, 10 and 5 seconds remaining, and then counting down the last 5 (no I did not simulate a buzzer on the occasions we had a violation :D ). This was challenging for a few reasons, and I hope that I never have to do it again.

"Foul Is On ..."
 

I hate it when the announcers say "The foul is on number twelve, it's his second, and the team's fourth", before I have reported the foul to the table. Happens all the time at two schools that we service.

Occasional PA
 

I do the PA as a fill in at our school, and work the book the rest of the time - which is why I don't have time to officiate.

I'll play music during timeouts for about 5 sec after the first horn, with a fade 2.5 sec fade out. If the teams are out early, the music will be stopped before the player reaches the OOB location.

I will call out 1 min remaining if I notice it. This is to help both the players and the officials (they will usually give the hand signals after the announcment)