No the cover does not affect the camera quality, its just a piece of glass. You might want to try and clean the camera lens with a q-tip. If that doesn't help then the lens itself might of gotten scratched with it being exposed.
Does sound like an issue with the charging port. Have you tried a new charger and cleaned the charging port on the device to make sure? The S3's are known to have charging port issues so this is not surprising, but unfortunately with this model it does require soldering and not an easy DIY job.
Its possible but its going to require some good technician skills, hot plate or heat gun and a thin wire called Molybdenum Wire. Its not going to be an easy job for a novice and you could take a chance of damaging the force flex sensor, another part not available for purchase right now. I would say having apple replace the device is the best solution till more parts become available or wait.