Lew - I have no confirmed Chinese Communist era auto pistol rounds with primer crimps. I don’t know about 7.9 x 57 - some retired Air Force Officer has my collection of those. : )
When I say “confirmed,” I am talking about confirmed to me. I have the 9 mm Para round headstamped HKP CJ 9x19. Common wisdom would tell me that the “HKP” means “Hong Kong Police,” and that the CJ is the same “CJ” that appeared on other Chinese 9 mm Para. Still, as I recall, when these showed up there was controversy, never to my knowledge put to rest, about what the HKP stood for and about whether or not these were Chinese. The number style of the 9 X 19 looks Chinese to me, but the green primer seal does not. The are what I call "all-brass: cartridges; that is, the primer cup, case and bullet jacket are all brass and that is typically Chinese. Unfortunately, especially in recent years, it is typically many other countries as well. This round has a well defined set of semi-circular (3) primer crimps.
I also have a 9 x 18 mm Chinese Makarov keychain dummy that has three straight-line primer crimps. I am assuming they were primer crimps, that is. One is pretty far from the edge of the primer pocket and certainly would not have performed its intended function if it was a primer crimp. The others are close enough to be just that. It is headstamped 81 66 but the odd thing is that an ordinary ball round of the same date does not have these marks. Further, the round has no primer cup, and the crimps (again, if that is what they are) could have nothing at all to do with the attachment of the small ring holding the larger key ring to the cartridge. There is also one single hole in the side of the case, and the bullet is normal GMCS RN FMJ bullet of Makarov shape, just to complete the record.
It is clear that primer crimps are not the norm on Chinese Communist era ammunition, at least that of pistol caliber.
I am not qualified to give an opinion on the 7.62 x 39 mm headstamp of general Iranian headstamp style, except to say they are not the only country that has used just a caliber and a date on the headstamp.