Does a plugged in 12v usb-charger use energy when no device is connected?
1) yes, how long that will take depends on how much it draws and how long between car uses.

2) yes, they use power, more or less depends on the design &amp; quality

3) Solve it by powering it from a fused accessory feed or ignition feed.

And, personally, I would do 3 whatever the power it draws...