Learn English – What does smooth mean here

In this case, aye almost certainly does mean always. For one thing it makes perfect sense contextually. Moreover, the connection with Scottish actually makes a lot of sense. We learn from Morag, in another answer, that aye is still used in Scotland. Even if it weren't, archaic English or Scottish would not be out of place in this song.

The Watson Family lived in the Appalachian Mountains, a region settled by Scottish and Irish immigrants. Difficulty of travel kept them functionally isolated, and the pre-radio music of that region is known for strong ties to old ballads of Scotland, England and Ireland. Here's a great radio piece about this history: http://hereandnow.wbur.org/2014/10/01/wayfaring-strangers-book

The corpus of Appalachian folk music also includes a lot of references to political roles that never really existed in the U.S. - Lords, ladies, knights, kings, etc. Examples abound here: http://www.contemplator.com/america/index.html

A "public worker" is someone who works for the government. It would include teachers at public schools (i.e. government-run schools), policemen, bureaucrats, etc.

"Public works" means government-run construction projects. So a public worker might well be involved in public works, but they also could be doing many other things.

I should clarify that this is American usage. I don't know if it's different in other English-speaking countries. I think it's the sort of word that might be.