Diamond Arms shotguns were made by several manufacturers, but if the rest of the patent date is '13', this one was by J. Stevens Arms and retailed by Shapleigh Hardware.
Not marked, Model 9
50-100 USD
The value of a 1905 model D single barrel choke bored Diamond Arms shotgun is actually dependent upon a number of things. Most importantly the condition of the shotgun.
Look up the Marlin shotgun with the same model number.
No published data
Impossible to answer without knowing who made it.
about $100
You will have to contact Browning.
No way to value with only the serial number and no other descripitve information.
I bought the same shotgun, serial number in the 91000s, for 50 dollars. Ones in good condition can go for 80 dollars. Unless, it is in perfect condition, 80 dollars is the max value.
The question can't be answered without knowing who made the shotgun. Even then, information may not have been published.
Approx. 1869 is when it was patented.