Battery calibration failure. Or you charged it while it was completely powered down (not sleeping or locked) the on-screen power off charge indicators lie. One of my ICS tablets doesn't even charge past 30% if the power is off completely, the big battery charge indicator will display full, but only give 30% power. Don't ask why. I suggest getting to where the phone is able to stay on. Then plug it in and let it charge while on. Then let it die completely, and repeat this cycle. This should recalibrate the battery indicator, and I suggest not turning the power off completely, just lock the screen where it is off but phone is on anyway, then plug it in each night.
Had an iPhone that did this often. It truly is annoying
The mobile network seems to be using some good amount of juice on your second screencap. Is your phone a CDMA phone? (Verizon, Sprint, Virgin mobile, Page Plus) are you often in a fringe or low/no service area? CDMA phones literally devour batteries and often get hot if they are in low or no signal mode. I never knew why
"If you treat your system like a kiln, don't be surprised when a brick comes out the other side."