Will rooting my phone improve its battery life?
The only way rooting can gain you battery time is if you can uninstall an app that's using a lot of power, and which you can't uninstall without rooting (i.e. it's something that shipped with the device). I don't know what is on your device, but judging from what I've seen on my Droid 3, there's not likely to be any noticeable change in battery life. On the plus side, if you root the device, you'll have the option to get rid of any junk that was pre-installed and thereby not have to see all the update notices for stuff that you'll never use and which wants more and more permissions with every update.