The price is what keeps people away from this gun. The gun may be OK for a third or a half of the advertised price.

My earlier hammerless guns have the serial number on the side of the lug in a much smaller font size, but on my 20-gauge VH-Grade of 1930 vintage the serial number is in a larger font size, though not quite as large as the gun in question.

The stamping on the frame, barrel lug and forend should match in size and style. As if they were stamped with the same set of stamps, because they likely would have been. This would be an indicator that all is as it was original built.

Stamps do vary in size and style over the years of manufacture.

Yes, barrel sets can be added at later times and would have been stamped with whatever style of stamp that was used at that later time. So variation would exist in that situation.

The stamping on these barrels is outside of any style that Parker used at any time and how poorly the numbers line up and the placement of them is another major clue to them not having any connection to the factory.