Why Does My iPhone 5s Shuts Off Even My Battery Is At 50 Percent? The Fix.
It sounds like you are have a battery that is going bad. I was told that batteries will start to do this around 3-4 years on some devices. My iPhone 5 had a depleted battery that expanded and I had to get the iPhone replaced by Apple for the cost of the battery. The bluish tint is a new one, but it could be related to the battery if it was starting to expand.
When I started to have issues with charging my iPhone 5, a hard reset would fix the battery showing the wrong percentage or not seeming to charge accurately. You may want to bring it into Apple if you can for a diagnostic on the battery, as it may qualify for one of their replacement programs, or they can replace the battery (or even the entire device in some circumstances) for $79.”