Yep, the fan and the usb will both get their power from the 12v and will still work. The actual inverter circuitry is separate and has almost certainly failed. Like a lot of electronic items these days the repair bill will be higher than buying a new one so unfortunately it's off to landfill!Probably and there is no reset switch and it's a sealed unit.
I was surprised it still works on the usb charger and the fan still goes.
I have to assume they are 2 different circuits working independently