, first issue sounds like a bad battery (hopefully, and not some charging circuit issue). I would replace the battery first. If after that you still get the iTunes error 1600, try this Get the latest version iTunes.
Check the USB cable is available and connect computer correctly.
Turn off the iPhone, and press the Home button until the USB cable connect the device.
Hold the Home button again until the "Connect to iTunes" message appears.
Release the Home button and restore required.
Connect the iPhone to PC via USB cable.
Run iTunes and backup your data.
Select "Shift+Restore", and then select the latest firmware from computer.
A message will pop up to inform you to erase and restore iPhone to iOS the latest cersion of iOS, and then click "Restore" to verify the restore with Apple. Also, check on here for more info. Hope this helps, good luck.