AK's use Berdan-primed ammo.......center-fire would have been a bit radical for the time.....the iron sights would have been not much better than what was available, certainly no better than Creedmoore sights. Think the AK would be tough enough to stand up to period lead- and black-powder fouling? That gas chamber might not last long before filling up with crud.
Turtledove makes a fairly good case that they could, given time. And if not the smiths in the South, with their limited industrial base, then the smiths in the north. He makes the analogy that if an Afghan gunsmith can manufacture AK copies with the crude tools he has in his Peshwar village then, eventually, an 1860s gunsmith could, once they knew it was possible.
Same thing applies to the powder and the clad bullets. Once you know a thing can be done someone will figure out a way to reproduce it. My guess is that it would have taken 10 years to produce a crude new autoloader based on the principles shown in the AK, and probably another 10 to get the powder. I don't have a guess how much technology is involved in manufacturing jacketed bullets, but I'm betting that would come in the least time of all.
Right now I'm reading a somewhat similar series of books. This starts with the books 1632 by Eric Flint and 1633 Eric Flint and David Weber (both available as free eBook downloads from Baen's free library). The premise here is somewhat similar to Guns of the South. In this case an entire West Virginia coal mining town and about 30 miles of surrounding countryside are switched with a similar sized chunk of Germany in the midst of the 30 years war (it happens, no real explanation except a vagure reference to a "cosmic shard"). This bunch of union coal miner hillbillies go out in their pick ups after this big flash happens to try to figure out what's going on. The road suddenly ends in this hill that didn't used to be there. They climb up over the hill and see some guys with long spears in odd outfits and funny metal hats sacking a primitive farm, torturing the farmer and raping his wife. The leader of the group looks back and says "Bill, you got your hunting rifle back in your truck?" You can guess the outcome of that little match up.
I'm on about the 7th book so far. Lots of fun. The trial of Galileo is particularly fun. And what they do with the music over the loudspeakers and then the napalm to the inquisition guys in that castle.... <g>
They go into the tech a lot in the collections of short stories. They have numerous articles where they discuss why they make certain tech choices, such as what type of ham radio set ups they go with because of the low sun-spot activity during this historic period. There are tons of people contributing to this now and it's grown to be quite a fascinating read. Allowing for the odd left turn of the story's premise the thing I like the best is how much real history they throw in.
This is what I read when I'm not reading technical manuals or IEEE papers. I need something I can totally just not worry about.
Where would they get the chrome to do the chamber and barrel?