Not sure if it will increase battery life, but it is the recommended way for the initial few charges Lithium Batteries. Incidentally, your battery will be quite poor for the first few charges, but it does get better.
It's pretty basic, but I actually think the in built music app is quite good. My only beef with it is the lack of Deezer integration, but I think that's a limitation of Deezer, not the music app itself.
I had a play with the poweramp trial yesterday and I have to say, with my headphones, I much prefer the Beats audio enhancements over whatever I could create in poweramp (it's still a cracking app though).