Well, it wouldn't be much of a song if it doesn't have any lyrics now, would it? XD
Seriously though, if あなた tell me about a song, I instantly assume that there is 歌う in it. If あなた tell me something about music, it could be anything...
it depends. songs are for singing, but instrumental songs are different... there, well, instrumental. so, its all depending on your definition of song.
I guess it depends on your definition of "song". To me, a song is words set to music. Otherwise, it's a tune, a melody, an instrumental. But like some of the others said, a tune can tell a story without words.