I'm no Parker expert, but.....
The utility grade Parker was the Trojan. Same action as the higher grades, same fit,just no ornamentation and plain wood sans checkering.
The higher grades were letters. I think the lowest was a V grade, and the highest letter grade was an AA. There were also some specialty grades with names. An H after the grade indicated a hammer gun, an E that it had ejectors.
Only three Parker Invincible grades were made.
Frames came in numbered sizes, the biggest was about a 6,intended for the big 4 and 6 gauges used by Waterfowlers, and the smallest a 000,IIRC.
For 16 gauge, you could order it on a 2,1 1/2, 1,or 1/2 size. Most were 1 or 1 1/2s.It should be stamped on the water table.
Galazan,DBA Connecticut Shotgun Manufacturing, sells replacement buttplates.
Finally, please have a qualified smith check your heirloom over before you shoot even one shell in it.
If the barrels are Damascus, it may be unsafe to fire. Hang it over the fireplace and admire it.
If the chambers are for shells shorter than those we use, pressures can destroy this fine old shotgun and maybe the shooter also. Short shells are available if it can be fired.
As for the ring, some shotguns do that and no probs. Others ring or more commonly buzz to indicate the barrels are separating.
You may want to google the name "Del Grego". Three generations of that family have been the go to folks for Parkers.
HTH.....