If this made sense I could answer better but if your asking for a date of a model 31 by serial you are better just looking at the date code stamp on the barrel. See related links for information on the Remington Society of America.
No such model in the Remington line.
1919
probably 200-400 depending on condition
Remington has never made a firearm with the model designation of 812
You will have to call Browning to find out.
Steel or Damascus barrels?
100-300 USD or so
Remington has made many thousands of 12 gauge shotguns in dozens of different models/configurations.
Contact Remington
A serial number might help.
do you have a picture
Remington Model 11-48 (Highest value) Made from 1949 to 1968: 425,000 were made. $300 for all gauges except the 28 gauge. 300 percent for the 28 gauge.