Admin Technical & Free Throw???
 

So here is the situation I had today. White shirt goes up for a layup and gets fouled. The shot goes in so I am about to administer the one free throw. A white team sub (#10) comes into the game. Before I give the ball to the shooter, the tables buzzes us over and says that #10 is not in the book. No problem, we have a technical on the white team. What's the order of administering the free throws? Should we have cleared the lane, let white shoot her one free throw, then allow blue to shoot the technical foul free throws and give the ball to blue at the division line?

NFHS: false double foul, administer in the order of occurrence. So, yes.

And, NCAA: Shoot the T first, then resume at POI (the FTs for the shooting foul).

So, the answer depends on the rules code being used, which wasn't specified in the OP.

If this was the second occurrence of a player not being in the book, say 5 game time minutes after the first time we had a player enter the game that was not in the book, do we still administer the technical foul on the second occurrence? Or is it just one technical foul and the second time this happens there is no technical?

Only 1 tech no matter how many times the book has to be corrected/changed. So no T for the second time you are adding a player.

Agree With Eastshire ...
 

Three scorebook situations: adding a name to the team roster, changing a name or a number in the official scorebook, and/or having a player change a uniform number, are penalized with a team technical foul when they occur, after the ten minute time limit. These infractions occur when the scorer is advised to add to or change the official scorebook. The foul must be charged when it occurs and enforced when the ball next becomes live. Once the ball becomes live, after such changes have been made to the scorebook, it is too late to penalize. Remember, the ball becomes live when: on a jump ball, the tossed ball leaves the referee’s hand; on a throw-in, it is at the disposal of the thrower; and on a free throw, it is at the disposal of the free thrower.

After the ten minute time limit a team is charged with a maximum of one technical foul regardless of how many infractions of the following are committed: changing a designated starter, adding a name to the team member list, requiring the scorer to change a team member’s or player’s number in the scorebook, requiring a player to change to the number in the scorebook, and/or having identical numbers on team members and/or players. Each player must wear the number indicated in the scorebook, or change the official scorebook number to that the player is wearing. Any additional substitutes who become players and require the changing of the number indicated for them in the official scorebook will not result in a penalty, as the one maximum technical has already been charged to the team for that team’s administrative infraction