1. What is the significance of " 1-1/8 " on the barrel flats? Obvious that was the nitro proof shot weight. Does it tell us any more?
That was the standard proof for a 2-1/2" chambered gun. The standard British 2-1/2" shell contained 1-1/16oz of shot and propelled it at about 1200 fps
2. What is the significance of " 1/31 " on the barrel flats?
That was the Diameter of the barrels at the time of proof. There is a table you can look up and see what the diameter at the time of proof was. In England it is illegal to sell a gun that has been honed a certain amount past the original proof diameter without reproofing the gun. It is not in the USA.
3. I didn't see any length designation on the barrel flats. Should it be there?
If you mean chamber length I believe the 12 over C in a diamond indicates 2-1/2" chambers. Over the 100 and some odd years they ahe been proofing guns the rules have changed from time to time. If you could post pictures of the barrel flats it would be very helpful
4. Is a well-restored moderately engraved Birmingham BLNE 12 gauge worth $3k? If I tired of it, would it be difficult to sell for that amount?
It is hard to say without pictures but that is a lot of money for a Birmey Boxlock.
Best,
Mike