Car audio question

You would need a very nice 12V power supply. The size of the power supply would depend on the size of the amplifier. I would highly doubt the car amplifier requires a 15A circuit. Most car amps are larger and less efficient than that. A small car battery would help give a little reserve capacitance but isn't 100% necessary depending on the power supply. Honestly, with the money you would put into a power supply you could get a cheap home receiver and it would be a far easier set up and more efficient. Car and home audio products are built very different because they are two completely different acoustical environments. Nonetheless, it is possible to do without blowing anything up.