To quote Louis Armstrong "All music is folk music. I never heard a horse sing."
Folk music is no more than the music of the ordinary people and has roots in every culture. There is no common root though modern communications have given us access to more sources throughout the world. It is the music of the hunting party, the victorious warrier, the farm labourer, the factory worker, the washer women, the drinking party. It is the music of festivals that mark significant events and the music of human relationships. It is a way of recording for posterity the stories of the people, their battles and their joy. It's history is unwritten because it predates writing.
Of course folk music has continued to develop over the years though was still not always written down even though literacy became common. Mostly, songs were learnt by sharing and listening and were passed on in much the same way, maybe changed a little at each transfer which is how we sometimes come to have many different versions of the same song.
The genre of music known as 'folk' spawned modern variants, inspired by the likes of Woody Guthrie, Pete Seeger, Cisco Huston and many others. Perhaps the best known is Bob Dylan whose style went on to depart from what many would regards as 'folk' but there were many others who continued with the traditional style of folk music from their own (or another) culture as well as those who followed a more modern, mass media based approach.
In any given culture, there may be particular instruments associated with the traditional peformance of the music of the simple people and there may well be rhythmic and tonal tradtions too. Since folk music has so many independent roots, it would be misleading to generalise. Some cultures might tend towards the easy comfort of a pentatonic scale while, to others, that would be too sparse and lacking in richness. Folk music predates guitars and banjos or any such complicated, expensive instruments. Originally it would have been the music of the voice and the stomping foot. Maybe, in more relaxed times, it would have included percussive instruments or basic plucked instruments. In modern times, it is easy to associate guitars, banjos, flageolets, pipes and so on with folk music though we have to be aware that is a very selective view of the world.
That is the challenge of defining folk music. It has no agreed definition and it has many intertwining threads of tradition. You could describe the characteristics of folk music from a particular culture but it would not necesarily be an accurate representation of the music from all cultures. In the end, what is or is not folk music comes down to a matter of opinion. Were Fairport Convention folk musicians and, if so, were the Rolling Stones? You could make a case for both.