vart,
I don't know the answers to the specific questions you're asking, but if an alternator is rotating, it should always be connected to a battery. This is because an alternator needs a voltage reference to prevent it's output voltage going too high and blowing all the diodes in it's diode bridge that converts the 3 phase AC to 'ripple' DC.
If an alternator spins without a voltage reference, residual magnetism in the exciter winding can generate enough voltage in the output windings to cause the above.