But I cannot import data to the stock fields: When I set up the correct product processor, I can't see the Stock field which is present in my product variation type.
As for me there was only one solution: reinstall. And after reinstalling first you should add importer, set stock mapping and only after that - enable feeds tamper. If I installed tamper before mapping setup there always was same problem with mapping. So, mb it's same thing. Sorry, can't comment.