I've only had the phone for a few days, but I'm already draining the battery like crazy.
I've turned on the batter life saver, but that's not enough.
What else can be done to improve battery life? I see a lot of apps running in the application manager that I don't use, but I'm hesitant to force stop them. Are there any that would be safe to force stop?
Well you could do this as I do with my 2 Phones, Tap & hold your button to right of your Home button if you have any apps that are running you should see them running in a Vertical Line with a swipe to the right or Left on your screen it will Safely stop the app running in the background.
A good app to use to see what your phone is Doing and I've use for years is System Panel app it is available as a Free app or for $2.99 it helps to show allot of what you phone is doing and what is and what is not running..