Q: Any way to manually manage music on iPhone 6s?

Any Apple nerds that can help me with a music issue on my iPhone? For some reason, I can't seem to totally clear out the music on my iPhone, and furthermore-when I add music to it through iTunes, it never shows up. Any way to manually manage music anymore?? When my iPhone is connected to iTunes, it shows that there is no music in my iPhone, but there is still a selection of 100 songs or so that seem to ALWAYS be hidden there. Any ideas?

Is it playing from iCloud? Anyway to turn iCloud off just for music app?