Re: rectifier
Not running voltage doesn't mean a thing, other than there's a battery there. Less than 13.5 or 14 VDC means a) rectifier smoked and/or b) stator smoked and/or c) wiring not good.
Start by measuring AC voltage from stator. Should typically be over 25 VAC. If not, replace stator and check again for good running DC at battery terminals. If over 13.5 VDC, you're good to go. If not the regulator/rectifier needs replacing also.
Be sure to note the difference between AC and DC above.
Regulator/rectifiier is the most common failure, but don't assume it's that without checking, unless you have a penchant for replacing parts.
Consult a shop manual fur where to check voltages.
