About the bluetooth...

cool, the issue ont he phone can possibly go to a faulty battery or a battery terminal; worst case will go to the whole power supply of the phone (Battery, terminal and charging capacitor;usually called the power IO)

you may try leaving the battery to drain out, leave it like that for at least over night, while it is off, charge it for about 4 hours max, then turn it back on. if this did not work, remove the battery check if it is swollen. and check the terminal if it is dirty, if so, just clean it with ethyl alcohol on a Qtip.