A little help, gentlemen

[BktBallRef]

"In the past week I had three different crews call this play differently and with different reasoning. This happened in Washington High School Baseball, I do not know if that matters or not. I believe that the first is correct, but would like your opinion.

An infielder (a pitcher in all three of my cases-either he was fielding a batted ball or he stepped back off the rubber and tried to pick a runner at first) throws the ball out of play.
Case 1- My batter was already safe at first on the play (on a batted ball), before the ball went out of play. He was awarded 2 bases and ended up on 3rd base.
Case 2- My runner was leading off of 1st base, the pitcher stepped back off the rubber and threw the ball out of play. The umpire awarded 2 bases and my runner ended up on 2nd base. It was explained that since the runner dove back to 1st base that was his 1st awarded base and his 2nd awarded base put him on 2nd base.
Case 3_ My batter was already safe at first on the play (on a batted ball), before the ball went out of play. He is awarded 2 bases and ends up on 2nd base. It was explained to me that the bases are awarded from were the runner was at the time of the throw and since he had not yet reached 1st base (at the time of the throw), 1st base was his 1st awarded base and 2nd base his 2nd awarded base. "

This should be NFHS rules. Thanks!