It seems like you are talking about two separate problems. Your first problem on how your phone does not display a charging symbol when plugged in could come from your phone charger or your phone's charging port. Try using a different charger, if that solves your problem your last charger is no longer working. If a new charger did not help your problem you will need to replace your charging port on your phone. For second problem with how your phone dies immediately after unplugging it from your charger is due to a faulty battery. There are no solutions to this other than replacing your phone's battery.

If the line is at the same spot in multiple photos it is possible that your camera lens has a scratch on it. To alleviate that problem it is needed for you to replace the camera lens.

It is possible that your button is getting stuck in your back casing when it does not come back up. When a hard button is pushed the connection to the motherboard may not be making contact correctly which can cause the button to not send the command.