Re: Very Odd Issue with the Battery.
Seeing battery percentage go up without being plugged in ins't necessarily a defect. Phones may read read slightly lower battery charge levels when the battery is being drained at a heavy rate.
Disclaimer: I'm usually pretty poor with analogies, but I'll try anyway. This information is to the best of my knowledge, and of experience working with similar batteries and power systems.
Imagine blowing up a balloon, and holding it closed between two fingers. This is your battery. Relaxing your fingers slightly to allow only a small stream of air out would equate to standard battery drain. You open the mouth of the balloon for two seconds only, letting out as much air as can get out in that time. This simulates heavy phone usage. The overall volume of air inside the balloon may not have dropped by a very large percentage, if you're reading the "charge" of the battery by measuring the pressure of air inside the balloon (read: electrons/electrons' flow rate), you may read a lower "charge" during those two seconds than is accurate. You can easily test this to try and replicate it. Turn LTE on, do what you can to lower your signal strength, turn the brightness up, play games, stream HD videos, etc. for somewhere around ten minutes. Heavy usage is your friend . Then, turn on airplane mode, clear all of your recent apps, and let the phone sit. Check your battery usage after a short while.