I think the international rules say that you fly the flag of the country
of registry (flag of convenience ?).

Yes.

Is it improper (illegal) to instead fly the flag of the owner's
nationality as long as a courtesy flag is flown under the spreader ?

Yes, that is improper.

You should fly your boat's national ensign. If you're a US boat, that would be
the stars and stripes.

If Grandpa happened to emigrate from East Undershirt and you feel compelled to
fly the East Undershirt flag, you'd treat it like a personal signal....same as
a yacht club burgee or etc.


Related question; are there any maritime law web sites for future
reference ?



Tried Google? It would be surprising if there isn't something out there.