Happened to us one time back in the early 90's. Field conditions were horrible -it was raining straight down, and field position was of prime importance. Team A kicked off to B, B fumbled, A recovered, scored. Team B's Coach chose to kick off to A to put the ball on their end. It worked - held them to 4th down, blocked the punt - (actually tackled the punter), scored, went for 2, made it - only scores of the entire game.

I'm using NFHS rules here.

Note the bold section. Team B is going to enforce the live-ball foul and take the points off the board so that they're still WINNING 35-30.

But, let's assume that by "live ball 15 yd foul" you meant something penalized as a dead ball foul (i.e. nonplayer or unsportsmanlike). Then the first two penalties mentioned may be taken on the kickoff.

Now go to the underlined section. By rule (NF 8-3-6), this penalty must be declined - there is no option to carry it over to the kickoff.

But again, let's assume you meant something treated like a DBF. Then that penalty is also assessed on the kickoff.

If A kicks off, they're kicking from their own 6.25-yd line. If B elects to kick off, they're kicking from the opponents' 15. With 15 seconds left, I think B is smarter to make A kick and try to return it - the risk of a touchback is too high.

Now, if there's 5 seconds left, then maybe the onside makes sense - the clock will only start when/if the other team touches it. But, in this increasingly improbably scenario, A now has a very smart play to make - they should step offsides. This moves the kickoff to the 10. Now there's no way to recover the onside kick - if it goes 10 yards, then it's in the EZ for a touchback.

So, the short answer is: yes, it COULD happen. But it would be stupid.

Well, if we're changing the OP so that it means what he meant it to mean, and you get this far... then when A "smartly" steps off-side, B would just as smartly decline the penalty. :)

After a spot is moved by penalty, can the team scored on rescind their choice of kicking or receving?

You would think.

I would actually guess not, but to my knowledge there is absolutely NO guidance on this (ridiculously obscure) question.

If they can, which I doubt, how would it work w.r.t. half the distance enforcements? Would you go back to the other team's 40 and apply all the distances serially again? If you just moved the spot 20 yards and reversed the kick-or-receive, because of half-the-distance enforcements it wouldn't always produce the same results as rewinding and starting over. That distinguishes this situation from an in-the-pocket choice of free kick or snap following a fair catch.

No.