The Nexus is very easy to root. Just be sure to read over the guide 2-3times or as much as you need, then go through and follow them. After, you'll be able to create nandroids so it's basically impossible to mess your phone up cause you can just go back and restore to a past date.
This has the official Android 4.0.4 so you have the update, and trust me, battery should improve quite a bit.
This has the official Android 4.0.4 so you have the update, and trust me, battery should improve quite a bit.