Retouching
 

I would like to ask for input on the following situations........

0 or 1 Outs, R1 is running on the pitch and halfway to third base when a fly ball is caught by the SS. The SS:
a) steps on 2B and indicates to the umpire that the runner needs to retouch his way back to 1B.
b) accidently steps on 2B before throwing the ball into the stands when attempting to throw the ball back to first base.

Neither of these is a proper appeal (I assume that's what you are asking about -- and not the award in (b)). The base left too soon (or the missed base or the runner) must be tagged -- you can't just tag an interim base that the runner must touch.

thanks, yes I wanted to know about tagging the non-original base.

End of call
 

So in regard to your OP. Say the SS steps on 2nd and defense thinks double play end of inning, so they toss the ball to mound and all run into dugout. The runner (returning) ..

1) Knows baseball, and goes all the way back to 1st and stops
2) also leaves the field of play.

Q1) Once everyone stops, what happens then? no defense and running on first. just call out the defense?

Q2) So is the runner out by abandonment in 2? Everyone left the field, but the runner is called out by abandonment and the SS does not get the assist for that out?

The umpire should signal (and call) safe when F6 steps on second, so your play is unlikely to happen.

If ti does, I am just fixing it and bringing everyone out -- by definition these are "unsophistiacted" teams, and I'm not penalizing anyone for this.

Indeed, this is not an appeal. The fielder could only appeal the runner leaving 1st base early, because the specific violation that the runner committed would have been leaving 1st base. If the fielder does anything else other than touch 1st base, I would not credit him with making an appeal, and would not call the batter out. I would do nothing, unless I was asked to call the runner out on appeal. If the defense appealed this to me, I would say that there is no appeal, and the runner is safe (with a signal).