They and similar items are made in one form or another across a huge part of Eastern Europe
Yes, on the territory of the former Commonwealth.
The origins are probably in the east, either Tatars or Chinese.
Could be Italian influence - together with many other things imported from Italy by Bona Sforza. I don't see Tatars eating dumplings. Its not a part of their cuisine.
Could be China,maybe Armenians but that is less likely than Bona.