How to remove music from iPhone

I feel like I've read EVERY article, and support page ever and nothing is helping me and I want to throw my phone out of the window.....

I want to do two different things.....

1) delete the phantom music that is on my iPhone that I've literally deleted off of everything yet, still plays. I cannot figure out how to remove said music from my phone as it says the music is NOT actually on, said phone, but if I go into my library on my phone, BOOM, there is it. The files have even been deleted OFF my computer.

2) I also want to remove the music that seems to just WANT to be on my phone. (see pictures attached) These songs I cant delete off my phone either, yet I have the settings for me to MANUALLY put music on my phone only and have not "checked" any specific playlist or songs.....

Please tell me there is something I can do, other than go insane!?