Yes, you can charge the animal camera with an external power supply. For the DC connection you need a 6V/1.5A adapter with 3.5mm (outside) and 1.3mm (inside) plug. 

So when it powers off, it goes into a sleep mode. That sleep mode doesn't require alot of power, but if you have it set to turn on if the camera detects vibrations, it uses the cars battery. Mine is plugged in all the time and it only powers on when I turn the car on or it feels vibrations. With the vibration setting, it will turn on when I open my car door. But if your power source isn't powered when the car shuts off, then it doesn't use any power, just what the camera has stored up. Hope that helps 

Touch is invalid during power-on, wait for normal power-on before operation. 2. Check whether the touchscreen is damaged, do not touch the screen with sharp objects, it is easy 

The camera needs to be set to function without an E-Mount lens attached. You can do this by changing the following camera setting: 'Menu' -> 'Setup' -> 'Release w/o Lens' -> 'Enable' (Exact naming and location of this option may change depending on camera model). If your lens does not have a manual aperture control ring, it will stop down to its smallest f/stop by default. 

Since it's a manual adapter , set camera "release shutter without lens" to enable when using the adapter for the first time, or the camera will fail to recognize the lens and the shutter may not be released. (Exact naming and location of this option may change depending on camera model).