The sad truth is, there is no managing your battery on a smart phone. You can try all kinds of crap as well as some of the magical battery saving apps, but you're going to get between 3 to 5 hours of on screen time. Unless you plan on streaming movies or playing games all day, your phone should get you through a day, possibly with a bump charge in your car on the way to or from work. If you don't get this, then you've downloaded some poorly written piece of crap free app that's eating up you juice. There's no need to turn your brightness down to 10%, or turn your wifi/gps or anything else on and off all day long...just use/enjoy your phone and don't obsess over how drained your battery is.
EDIT: I forgot to actually answer your questions: As someone stated earlier, I would leave the Gmail updating alone. It's not going to have any noticeable effect on your battery and it works great as is. Regarding the multi tasking issue, what is it that you are wanting to do? The bottom right button shows recent apps. If you want to bring one to the screen, touch it. If you want to make some go away, swipe them to the right. If you're trying to use that button to manage your battery (thinking that you're closing unnecessary apps) you're probably wasting more battery (via the screen time) trying to keep stuff off the list, than you accomplish by getting rid of them.