1) The songs give everyone in your party a Crit-buff aswell as enabling you to use Troubador (for mitigation) and Battle Voice (for a DH-buff) - so even if you dont have dots up (what you should, adressing that later), it helps your party to keep them up.
2) Songs are OGC - that means using them doesnt cost you any other action. And they deal damage. You can weave them in without losing anything.
3) Mages Ballad is great when it comes to mass-pulls and AoEs, since every proc there equals a Rain of Death - so extra AoE-damage. For the above reasons you should obviously use your other songs aswell too though. Everytime you're wasting your chance to proc Rain of Death, you're losing another chance to shooting every enemy at once without using TP and between cooldowns.

To answer your question regarding dots: Yes. You should always be putting dots on enemies. Personally, I'm putting my dots on 3-4 enemies. I'm not sure if thats really 100% ideal, but I'm fishing for as many Rain of Death procs as possible. Obviously you want to prefer those mobs with more HP, so your dots will last longer, giving you more procs.

Rule of Thumb is that you wanna AoE with 4+ enemies on most classes.