NFHS says free throws for a technical foul, that was assessed after time expired, should not be shot unless it will effect the game. If the score is tied, the extra period should begin with the free throws. The rule doesn't address the situation where team A leads team B by one point. Am I correct to assume that team B would be awarded both free throws and if both are made the game is over. I hope I never have this situation.

As the free throws may possibly affect the outcome of the game, both free throws would be shot. If only one is made, then there would be an overtime period. Now my question is, based upon that situation, and the free throws being shot for a technical foul, does the overtime period start with the awarding of the ball to the team shooting the free throws and establishment of alternate possession?

I believe in this case, where A leads B by 1 point, and A is dinged, B shots two free throws as part of the 4th quarter. Should both go in, B wins. If one goes in, the game goes to OT. The OT begins with a jump ball. I believe the additional aspect of the technical foul penalty is lost. Ie. B is not awarded the ball OOB. OT proceeds as usual.

No. No part of a penalty may be carried over to the next period. 5-6-3. Start the OT with a jump ball.

Just a nit -- That rule (start the OT with the throws) applies if the T occurs after the ball is dead -- not after time expires. There could be a difference.