All of these are great suggests. I might add also, not to limit yourself to picking out the rythme, lead, licks, etc. for guitar. Practice trying to pick out the other instruments in song, such as, trumpet, piano, etc. using the guitar. These parts of the song have to be played as well for it to sound right.

As for the tune in your head. The first thing I would do is to record yourself humming or singing it. In time you will forget it and it could be a master piece lost forever.

The same goes for lyric lines that come to you from a deep sleep or talking with someone.

Record it and then work on it.