No a cigarette lighter outlet can not be installed on a snow machine without a battery. The outlet will have no way to charge up.
no
Yes! You can buy trickle chargers that work through the cigarette lighter.
what holds the the cigarette lighter in place once it is installed
If the car is left sitting for a long time and not running, yes. In some cars the cigarette lighter wont work unless the car is on for this reason.
Through the cigarette lighter.
If the cigarette lighter would normally work without turning on the ignition, yes.
Yes
yes there is a flameless lighter, it works the same as a toaster or a coil stove top.
No, because you are only connected to the power system when plugged into the cigarette lighter. The cigarette lighter does not play music. You need to be connected to the speakers.
You might be pulling too much power through the cigarette lighter. Also the cigarette lighter may grounding out for some reason or another. If the car has an aftermarket stereo, whoever installed it may have miswired it.
In the engine on the driver's side, underneath the battery cover.
have the alternator tested. I bought a cheap tester that you plug into the cigarette lighter that tells me whether the alternator is charging. I got this at the auto parts store 7T77T7