Hmmm. Mostly, ask a lawyer for question 2 and 3.

A real folk tune wouldn't be copyrighted, though modern (within the last 100 years) tunes might be.

In general, for question 3, and 4, there are no rules, as parodies are made all the time.

As for question 5 and 6, you probably could, but credit must be given. There are a number of church songs in United Church of Canada and I'm told in Catholic hymnals which have folk tunes as their basis. But credit is given to the anonymous person by saying that the tune is "xxx". There are a number of songs which come from Iona which use ancient folk tunes like that.