IPhone 6 battery suddenly dying faster?

Quick background:
I have the iPhone 6 (not plus), Sprint, 128GB, black front, iOS 8.3.
I'm very OCD about my battery percentage on my phone, I always have been. I'm in high school and my first hour is in a new building that had recently been built on campus and there's no signal ( I know bad signal kills battery). But, normally with my phone on airplane mode and grayscale, only listening to music for 40 min. And by the end of 1st period my phone would only be at 93% AT THE LOWEST.
As of last weekend however, my phone in 1st period (airplane, gray, NO music) without doing a single thing, goes down to 85%.
Dying quickly by the end of my 6hr school day.
Last night I went to bed at about 11pm with a battery of 41%, and I woke up at about 1am (2 hours later) and it was only at 80%. So, not only is it dying faster for no reason now, it's also not charging as fast as it used to. As well as going down in battery while in use on the charger.
Now, yes I have downloaded apps and whatnot, but I know it's not an app because it started over a weekend when I didn't do anything different. I have not changed my patterns of battery saving for 6 months in having this phone.

IOS 8.3 update for iPhone 5s?

Ok so I really want yo update my iPhone but there's not enough space to. So what do I get rid of or eliminate to have space so I can update my phone?

Where did the add playlist selection go?

Iv got an iPhone 5. When I 1st got a made a playlist but then deleted it. Now when I go into playlist down the bottom it doesn't show the add playlist button with the plus sign. So I can't make any playlists. I even reset my phone but it didn't come back.