The unaccompanied traditional song
Some thoughts - sorry these aren't fully worked out yet!
The song should have a Narrative - or at least a range of different characters or emotions.
Pitch range should increase with grade.
The musical difficulty should increase with grade: changes of time signature, leaps, modal settings, and other awkwardnesses will allow the singer to demonstrate what they can do.
That is why I discourage Scarborough Fair - it doesn't have a story, or any range of character or emotion. It isn't easy enough for the early grades (the modality and the pitch range make it really quite difficult)
Since I teach in Great Britain, I only use folk songs from England, Scotland, Wales and Ireland - mostly from England.
The new books from Faber (The Language of Folk) are good, but focus heavily on the North East. The have good advice about ornamentation (which I don't currently follow), and include a CD of demonstration performances.
I have a range of books of folk songs. TO FOLLOW.
Advice on performance: no need to sing strictly in time - treat the song like a romantic-era art song: convey the meaning of the text by slowing down or speeding up; don't forget about dynamics.
Here is a useful article, not all of which I agree with (!) from the ABRSM in-house magazine. (Knowing how things sometimes disappear from the web, I've taken the liberty of copying the text.)