Punt and step
 

NFHS

Team K punts the football. R1 does not field the punt and it is rolling to a stop. K2 steps on the football to stop it from rolling then both teams head for their sidelines. After a couple seconds I blow the whistle.

Is this considered downing a punt? What would you do?

2-24-2 A kick ends when a player gains possession or when the ball
becomes dead while not in player possession.

No, this is not considered "downing" a punt, however you were correct to blow the play dead when no player attempted to secure possession (4-2-2-e-2).

2-44: Touching refers to any contact with the ball, i.e., either by touching or being touched by it. Touching by an official in the field of play or end zone is ignored.

You just had first touching by K. Wasn't dead til you saw that no one was trying to secure possession.

Canadian Ruling
 

CANADIAN RULING:

Flag thrown for possible 15-yard RZ foul. If K2 was onside, it will be picked up. And both teams wouldn't head for their benches when K touches the ball.

phansen,

In your scenario, what could have R done after K stepped on the ball?

What is the benefit of first touching for R?

I want to make sure I understand since I'll be BJ in a couple weeks for the first time...

An R player could (with the ball just laying there) attempt to secure possession after the K player taps it with his foot. Since there is first touching by K in this case, if such an attempt were to be made, we would need a bean bag. Since R could pick it up and advance, the line gained through advancing would be the next spot, but if R picks it up, fumbles, or runs and is downed behind the first touching spot, we will need the first touching spot since that's where R will want to take the ball to start their series.

Remember that R loses their right to the spot of first touching if they commit a foul after touching the ball or if the penalty for any foul committed during the down is accepted.

If R would have picked up the ball immediately before I blew my whistle, I would have let them advance and bagged the spot.

Had a similar play years ago - punt rolling, K player stepped on it, but it rolled once or twice. R picked it up and returned it 80 yards. K coach is screaming at me, of course. The K player comes to the sideline, and the coach starts screaming at him, "I told you not to do that. That's the third time that's happened this year!" I turned to the coach and told him he had to make up his mind about which of us to yell at. He laughed at me, and went back to yelling at the kid.

Downing means you control the ball.

If K2 was onside, does his stepping on the ball produce a dribble? Or is that only if he uses a surface other than the sole of his shoe?

Yes.

But K2 is by definition onside for this Open Field "Kick", and can therefore recover without penalty. I would interpret that he may continue to keep his foot on the ball, partially because there is nothing that says he can't. :)