Does the rules govern what is to be or should be said during administration of a free throw?

Most officials I observe and work all do the same routine in the lane. Same verbals. Is this mandated or habit?

Not much to say, Ref Daddy. You're supposed to verbalize the shots and signal.

"Two!" Signal and bounce the ball.

That's all that's required that I know of.

The rules don't but the officials manual does.

I hate working with a partner who gives a clnic everytime there is a free throw situation. "OK, Ladies (Gentlemen), white under, white black, white. Watch your feet. Two shots. Freeze for the first one. OK. Two." (bounce, finally) Or, "one and one, play the miss, don't go over until the ball hits the rim. OK, Ladies, one and one."
Bounce, snore (by me).
There should be no instructions to HS players, IMO.

A number of areas do not have school sponsored basketball below the below HS level. So, it is at the Frosh and JV levels where these kids get there first professional coaching (term used loosely.) While your partner may have gone a bit far, IMO it always pays to point out the 1 and 1, don’t move, and watch your feet as a bit of preventive officiating.

I've been told to say as little as possible to the players (by officials and camp instructors much higher up than myself).

1 and 1: "1 and 1"
2 shots: "2" (regardless of shooting foul or double bonus)
Back end of a 1 and 1 or second shot: 1 only

PS this may be a midwest thing.

IMO the players should know the situation and when they can/cannot move on a throw. This is called being well coached (maybe an oxy) :D and having their head in the game

I do the same thing.

I only add "Let it hit." as a reminder of when they can move. Still short and sweet.