Should I Assume This Play Is Illegal in the States?
 

Happened in Canada. Kid caught a punt and immediately punted it back . Ball was picked up by his own team and ran in for a TD.

Should I assume a)it's not the same in the US and b)that would be a penalty?

Return kicks in NFHS and NCAA are illegal. In NCAA it'd be a 5 yard penalty and the ball would be dead at the spot of the return kick.

One thing the Canadian game isn't is boring.

Yes and yes- NF 6-2-1

I think return kicks may have been legal in the early days of football.

The penalty for R's illegal kick would be 15 yards.

It might not be enforced, however: R's illegal kick is treated as a fumble. There are a variety of scenarios here (R kicks pre- or post-possession, K or R recovers the ensuing "fumble," etc.). Here are a couple:

Play 1: K punts past the NZ, R kicks the ball pre-possession from the ground, K recovers. The penalty for IK during this loose-ball play would be enforced from the previous spot, 15 yards, and the down replayed (or 1/10 if past the LTG).

Play 2: K punts past the NZ, R kicks the ball pre-possession from the ground, R recovers. This IK foul qualifies as PSK and would be enforced from the spot of the foul (which I'm assuming is behind the end of the kick, where R finally recovered the ball).

Play 3: K punts past the NZ, R catches the kick and punts it back, K recovers. In this case K would have to decline the penalty for IK to keep possession.

Play 4: K punts past the NZ, R catches the kick and punts it back, R recovers. This post-possession foul is not PSK, but would still be enforced from the end of the "run" (which is also the spot of the foul).

There are numerous other variations (K's punt is blocked and R kicks it behind the NZ, it does/does not cross the NZ...).

Yes. The last major USAn code to ban the return kick was NFL's. Before that, Fed. The earliest ban on it was NCAA's.

Also banned by the USAn codes is onside recovery & advance of a live ball kick.

In fact, by now all the USAn codes have prohibited all live ball kicks other than from in or behind the neutral zone during play from scrimmage before a change of possession, NFL again being the last to do so. One thing that simplified was the administration of play following a blocked kick, by getting rid of the possibility of a blocked kick during a return or from beyond the neutral zone.

Or ... If IK enforcement leaves the ball short of the LTG, K can decline the IK and they take the result of the play ... 1st & 10 for K where they were downed (because R touched the kick beyond the NZ).

I assume the extra kicks are only illegal if they're intentional. Right?

The various codes have definitions of "kicking the ball" that make clear they're not about accidental striking of a ball with a foot. Usually, though, that comes up only in determinations where a loose ball was kicked. It'd be an extremely rare event that someone would accidentally drop the ball as for a punt or drop kick and then accidentally kick it -- or to crouch, place the ball on the ground, and accidentally kick it or have it accidentally kicked!

Right. Judgment call, but quite seldom a difficult one.