People ask "What sort of songs do you sing?" I say "Songs with the word - elbow - in them" or any other unlikely word I can think of at the time. Sometimes I say "Sad songs. Story songs. Silly songs."
As to pianos - folk communities singing what all of us would probably agree was genuine folk song used them when they were available and any other instrument that happened to turn up. Did that change the definition of folkmusic?