Yes, of course it would be of great help to listen to songs first, because then, when you really knuckle down and study the grammar you will find it easier, because you've already seen much of it in an indirect way when going through the songs. I recommend listening to the songs with the lyrics in front of you, and go over and over again till you get the exact accent and until you understand all they say without looking at the lyrics. I recommend listening to pop music, especially romantic pop music songs, because they have more lyrics and are more slow and therefore more understandable.

I hope you can understand my english :) The first thing you should do to improve is study grammar and later, listen songs to improve the pronunciation and the listening. You can take notes about the vocabulary and his uses.

Of course it will be helpful, but it depends on the songs!!! Some of them are really good, but others aren't worth listening to (from a linguistic point of view). What songs are you listening to? In any case, it's a good idea to learn vocabulary through music, but you should also try thematic lists. And grammar! Don't forget the grammar! :) ¡Un saludo!