Yes, As long as your headphones have a micro USB interface, it’s fine. 

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 

Hello, thank you for your question, in general it is possible to charge the Chillest GoSun cooler, please check if the charging port of your device is the same as the DC charging port we prepared for you, thank you! 

Yes, you can make calls. They also turn themselves on when you take them out. 

Yes.