It's true that deleting a Playlist from and iOS device will also delete the playlist from iTunes. However that does not delete the music from the cloud, nor, in my experience does deleting the playlist actually delete the music downloaded to the iDevice. I suggest that so see just the music that has been downloaded to the iDevice you go to Settings > Music and set "show all music" to OFF. This will display only the tracks that have been downloaded to your iDevice.
As to how to delete music... you can simply swipe across individual songs and tap delete. Or tap-n-hold on any Album or Artist and tape the "x" to delete. It is possible to delete all music from the iDevice by going to Settings > General > Usage and tapping Music, then swiping across and tapping the delete button.