I can't delete downloaded songs from my iTunes library

My master iTunes is on a Lenova thinkpad, but I also have my library on my iPhone and iPad. Downloaded songs have a little cloud with an arrow next to the title. When I try to delete them, it goes through all the screens, but the song remains on the list. I don't want to hide a particular song, I want to delete it. To the best of my knowledge, I am not signed up for Match. I don't pay for it at least. I am a complete novice so can anyone explain how to delete songs that I no longer want and are just taking up storage space on my iPhone 5s?

Also, I don't need music on my iPad version 9.3.5. Can I delete the library from the iPad without deleting my library from the other two devices (iPhone and Thinkpad)?