Hair is not self made, just edited together 4-5 MMD hairstyles that I liked and then re-rigged them to work together. The skirt should not mess with the hair, they're entirely different materials. Just tested in a new Unity project with the download available here. Probably user error. Will provide the correct skirt texture above though. The one in the project is older.
No idea. Shader really isn't important anyway. It just has a toon shader with an off-white color in the screenshots. Could achieve same look with standard shader.