The camera not functioning is most likely due to internal issues with the camera. The only way to fix this issue is to replace the camera. If the lens is not broken, it means that the camera is not working and has to be replaced.
This problem can be due to a couple things. First you want to take a look at your charging ports and wall connectors make sure those are working properly and are not the problem. Also you want to make sure your charging port is clear of any dust that is impeding any contact to your connector.
The reason for the battery not lasting the amount expected is because the battery is faulty or other charging components arent working properly. Other problems that can also cause this include having dust inside your vents which can be fixed by cleaning out the vents and cause the fans to work properly. Another problem that should be revised before changing your battery should be to try and change the charging ports and wall ports to make sure those charging options arent the problem. The battery over time loses its charging capabilities and causes battery to work harder and in result start to overheat. We suggest replacing the battery if these are not solutions.