Q: Songs

Hello, igerman. 

Thank you for visiting Apple Support Communities.

Here are the steps on how to delete music from your iPhone.

iPhone, iPad, or iPod touch

Before you delete, find out if you'll be able to download the song you deleted again (it depends on where you live). To delete a song:

1. Tap the Music app.
2. Tap the Songs category.
3. Swipe left to right over the song you want to delete.
4. Tap Delete.

How to delete content you've downloaded from the iTunes Store, App Store, iBooks Store, or Mac App Store

http://support.apple.com/kb/HT5772

If you wish to remove all music from your device, navigate to Settings > General > Usage > Music > Edit then the delete icon. 

Cheers,

Jason H.

igerman,

For some reason the information I provided is not accurate with iOS 7 and I apologize and will have that corrected.  You will need to swipe from right to left on a song in song view. 

-Jason H.