In the original post, it seems like "oral tradition" is contrasted with "literate transmission" as if the only variable changed is the manner of communication (oral vs. literate), but tradition and transmission are not the same thing. Transmission is how things are passed between people. Tradition is a process of recycling of preexisting materials to meet present needs (often with changes). The answer to both of the questions is we don't have enough information, although I'm inclined to answer yes in the second case, since I take it that singing in pubs and singing lullabies are traditional practices.
My impression of Buchan's work is that he was writing about people who were in primarily an oral society. But people in literate societies can still transmit things orally (and change them to meet present needs). They just might not use the same kinds of formulaic structures that Buchan writes about.