Yeah, and how does one usually combine snälla with tack? I know it's done, I just don't really understand when or why. Tack snälla is basically thank you kindly I suppose, but are there some other very common variations?
Yes, we say Tack snälla, but I don't remember any other variation. I would say that it is short for "Tack snälla (du)", telling the kind person that he/she is very 'kind', doing whatever I thanked for. "Thanks, you are so kind!"
Is it really a cognate? Or just a False Friend? When I was a child we had "Snälltåg" which had nothing to do with being kind. It meant 'Fast train' from the German 'schnell'. We used to have a stronger bond to German language, lending words, for centuries.