I can't answer most questions, I am way too young and I don't think of the Weavers as folk music at all, but instead as a pop bastardization of folk music.
I doubt Hank Williams ever considered himself folk.Hindsight would call Country music a folk tradition, but, with the exception of Johnny Cash, later, I doubt any Country singer considered himself a Folk singer back then. Hank was certainly embraced by the one strain of American Folk music which most clearly defines the quasi-definition of "folk", the Woody Guthrie strain. I know the Weavers are suppose to fit there , but to my ears they don't, their "So Long It's Been Good To Know You" makes me cringe.
"Ramblin" Jack's biggest contribution was teaching Dylan. Dylan acctually sounds more like Jack than he does like Woody. Woody was in no condition to teach Dylan when they met.Although Jack imitated Woody , Jack was far more proficient of a flat picker and it his guitar style Dylan emulated. I am not sure Jack had a great deal of success beyond those "in the know". I could be wrong, he certainly deserves me to be wrong.
I am eager to read other contributions to this thread.