Play:
Scrimmage kick play where K commits a foul for illegal motion. Kick then rolls out of bounds 30 yards down field. R accepts the penalty and forces K to rekick. When does the clock start and why?

Thanks

Depends on the rules code.
For NCAA, on the snap since we just had a legal kick play.
For NFHS, it would be on the ready since a new series has not been awarded to either team.

For NF: I was under the impression that, after a penalty, the clock starts as a result of what happened during that down. If the kick went out of bounds, then the clock wouldn't start until the snap. Am I thinking of the wrong down? What would happen if on third down, the clock was stopped and this situation happened on 4th down?

I am confused about when the clock stops and starts following a penalty. Any help on understanding this would be GREATLY appreciated!

I missed the OOB part, that is the reason for stopping the clock. No change for NCAA, but that now is a reason for starting the clock on the snap for NFHS on the replay of the kick down.