From your Spine project, you seem to have become quite confused. I encourage you to start from a simpler setup to understand the workflow of creating animations with Spine. Anyway, I have created a simple example project to help you achieve what you want to do, so please check the attached file:
hairtest_0201_re.spine
Your project had a lot of bones, and some bone directions of them were not aligned with the direction of the hair, which made it difficult to animate it. While it is possible to animate with paths as you attempted, such a complex setup should not normally be necessary to sway hairs.
The project above includes a simple hair swaying animation, but if this is not the animation you would like to achieve, please describe to us what behavior you would like to see.
Since you seem to have a misconception about the setup workflow in Spine, you might want to watch tutorial videos we have published. I think "Flour Sack Rig - Spine Tips #4" is the most concise video we currently have available that shows the setup procedure, so it would be helpful to understand the basics of Spine:
