Welcome! For music, I use both Doubletwist and PowerAmp. I have an iPod and I also like to organize music in Windows Media Player. I've found that PowerAmp blows away the sound quality of my iPod so I've been using my dinc and TB for my music player more now. With Doubletwist, the desktop app lets you import playlists from both players (iTunes and WMP), then you can easily sync the combined music over to your TB. Then after syncing, PowerAmp will recognize the playlists that DoubleTwist just imported. I'm pretty picky when it comes to sound quality and I have not found a player that sounds better than PowerAmp. Just my opinion.
For battery, I too have found that if I disable the 4G I am able to get the same battery life as my old Incredible. I just discovered this the past couple of days which was a total life saver. I fell in love with this phone but it made me really sad to think about returning it because of the batter life. Knowing that I am able to extend the life pretty substantially has just made me love it even more. The app I use to toggle between LTE and CDMA quite easily is LTE OnOff. It's one of the few (if not only) free app that can let you toggle this setting so easily.
Hope this helps.