" but also songs he had written himself"
Been there done that - the ones he wrote weren't folk songs and he would have been the last person to have claimed they were.
A nerw song is a new song - it graduates to belg a folk song through a process of natural selection (only we refer to it as the folk process)
"It's still the same song"
It has undergone the process of selection , which by and large, no longer exists - the music industry helped to put paid to that.
"...does that make them 'folk' and if not, what are they?"
You tell me - what makes them folk?
" the current number one could become a folk song if people are still singing it in, say, 100 years time"
Nope - it would still belong to the feller who wrote it and almost certainly copyrighted it - he's have made sure of that.
Is God Save the Queen a folk song - it was written a long time ago?
Is Ode to Joy a folk song - even older?
"folk' is about a style that maintains a tradition and not about age?"
Nothing to do with style otherwise all folk songs would have been made in the same style - they most certainly are not
Jim Carroll