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 

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Yes, there is a metal piece at the bottom center that you can probably hang a weight from.  

It is at the bottom of the center column 

I was able to stow my camera including the battery grip in my backpack without any problems. Because your tripod is 1m high, it looks a bit strange on this backpack. Unfortunately, you only have limited space on the side for attachment. Hope could help you