A-ko, you can't plug a battery straight into an AC system, it will freak out. Gotta run the current through a rectifier to convert it to DC, and a preferably regulator to keep it from overcharging.
The _flywheel_ spins under the flywheel cover, hence the name. The coils are underneath the flywheel. There are already wires coming out of them leading to the various things that they power, eg. headlight, tail lights. Get a wiring diagram, it will be muchos helpful.