Re: If I root, can I do something to help battery life?
Well... if you root, you CAN increase time between charges.... but it takes a little bit of effort and research. I was never a big fan of those battery saver applications, even the Qualcomm one. I found them to be heavy handed, all or nothing solutions. I choose a different route, choosing instead to do my own thing... I used Tasker along with a few other supporting tools (Secure Settings, Google Consent Disable Xposed module, Synker)....
For screen on stuff, the biggest gains are from underclocking and undervolting (the latter might get a little twitchy).... Franco's 'Per App Mode' feature that comes with his paid-for FKU app is great... throttling down the phone when you are running apps that don't need full power... You can underclock your phone and only kick it into high gear when you play a game or need processing power....
But I found that there was a lot to gain if you managed your phone's function when the screen was off. And that is pretty much what those battery saver apps do.. If left to its own devices, all those background functions can really put a dent in your battery.... idle drains of 4 or 5% an hour are not uncommon... and that really adds up over the course of the day. Things like Google Now, Facebook, Google+, etc... they all can wake up your phone often, taking your phone out of deep sleep and eating your battery. I used Tasker to do things like disable Google Location Services when I was at home or at my office, turning them on only when I was out and about (or for a little bit in the morning and afternoon to get my commute traffic reports).... setting it so Gmail was the only one that would sync, on a schedule, in the background when the phone was idle (screen off). So when I'm sitting at home or in my office and my phone was off, it was sleeping like a baby using next to no power. If I left it on my desk at work, it would only drain like 5% over the course of a work day.... MUCH better than the 30-40% that it would if I did nothing and left it do its thing.
I actually want to write my own app to do all this and make things a bit easier, but it would be a bit on the complex side due to what it would have to do.... but the end result is that once I ironed out the kinks, I would see a considerable reduction in my idle drain....
Now, this is by no means an easy task.... I've been developing my approach for almost two years now, going back to my old Galaxy Stellar.