second going to third

[eureka25]

Here is the sitch:

R1, no outs, 12 year-olds, OBR. R1 goes to steal second and Batter hits deep fly to right center. R1 gets to second base. R1 now "thinks" the ball is caught and takes 2 hard steps back towards first. Now realizing ball is not caught, he immediately goes to third without touching second. Defense gets the ball back into play.

These are the questions I have.
a) Does he need to re-acquire second again to go to third
b) Does "intent" of running back to 1st, make R1 have to re-acquire second.
c) What if ball was thrown out of play - did R1 own second base regardless of how far he ran back to first.

I know this goes back to a thread of running the bases in the wrong direction. This just has a little twist to it.

BTW - This was something I saw and no appeal was made - so nothing was done. Just had me thinking now it will happen again and want to be prepared.

Thanks,
Jeff