1. Most new cars come with accessory power port aka cigarette lighter, there is very little differences, both supply 12 volt power from the plug, it is how it transfer the power that makes it a cig lighter or a power source.
2. Your GPS or cell phone will have a voltage reducer that will reduce the voltage from 12 volts to 5 volts for most electronic devices these days.
3. The cig lighter plug heats up much like your counter top stove that have the coils, it does not have fires but builds up heat through supplying power to ground creating aresistantt that gets red hot.

1. If he can build a circuit to limit the amperage, then yes. otherwise the 40 Amps cranking power of a car battery will cook your pump and maybe your breast.
2. The lighter socket only comes with wires. The circuit will need resistors to set up the circuit properly.

First you need to get a 12 volt lantern battery, that will provide all you need. they have a large capacity. second. the wattage is actually based on the fuse. a 20 amp fuse gives 240 watts. Ohms law - Volts x Amps = Watts, a 25 amp fuse gives 300 watts, and so on. your mp3 adapter prolly uses very little power 50 to 100 watts, so you should be ok using a lantern battery. if you wanted to pack 8 AA batteries together, you could also do it that way, however, it will drain those 8 before it would drain the one lantern battery. if you do decide to go with 8 AA or 8 c's or 8 d's, (all will give 12 volts and enough current) go to radioshack and ask for the appropriate battery holders. this will make the project neater.