FWIW, the generator on the Fazer (and most bikes) is a magneto i.e. an alternator using permanent magnets. The term alternator just means ac generator, but is generally used to refer to those that use electromagnets rather than permanent ones to provide the magnetic field: they're bulkier but more efficient and are what cars use.
In theory, disconnecting the battery while the engine is running needn't cause a disaster. The regulator will continue to limit the peak voltage and, while the rectified ac will be very lumpy without a battery, the ignition should cope. However, it's not something I'd care to try and I agree with all the advice you've been given: as a diagnostic technique it stinks. If the regulation had failed volts could rise high enough to nuke the ignition unit and instruments.
The stator coils should measure 0.36 to 0.44 ohms so yes, yours sound about right (you'll probably be within spec if you subtract the measurement you get when shorting the multimeter leads together).
If the battery charger you used as a supply is a simple transformer and rectifier type, then the volts dipping to zero fifty or a hundred times a second would probably have starved the ignition and that is what stopped the engine in your test.
Provided there's decent continuity in the rest of the charging circuit then I'd agree the rectifier is probably to blame.
The easiest way to check is by substitution. I've never tried testing mine, my Yamaha manual doesn't give details, but if is a simple bridge rectifier and shunt regulator arrangement it should be easy to check. On the other hand, if it uses SCRs in the bridge to reduce the power the thing has to dissipate when the magneto is at full output I'll agree with Mr Haynes that it's too complicated to test with a multimeter.
