There is usually a serial number or a symbol stamped into the side of every carburetor. Unfortunately the only way to know is to match this up or find someone who recognizes these markings. Sometimes a web search can identify a serial number.
unicycle, wheel barrel come to mind
Trade name, 50-100 USD
This version of the company name indicates manufacture between 1886 and 1916. The Electrosteel mark suggests sometime after 1900. Don't know about a barrel, but you can probably find a whole gun for about $75. Might find one at a local gun show, in a pawn shop, or one of the online auction sites.
HD Folsom/Crescent made both single-barrel and double-barrel shotguns using the Whippet name for Hibbard, Spencer and Bartlett (huge hardware catalog store in Chicago) from around 1900 until the late 1920's. If the gun is a single-shot, value is going to top out at $100. Double-barrel .410 shotguns like yours can reach over $400-$500 if in excellent condition. sales@countrygunsmith.net
If you google that name you will find several persons of that name. So there is no single answer.
A barrel maker is a person that has a skill for making wooden barrels. Another name for a barrel maker is a cooper.
A bayonet is the name of a knife attached to the barrel of a rifle.
It's just called a barrel.
The name with "Tool Co" at the end was only used from 1887 - 1916.
Belknap Hardware- along with many others, sold shotguns made under their name by Crescent Firearms.
American Gun Co was a trade name used by H&D Folsom, usually found on single and double barrel shotguns c. 1880-1920. The company began operation about 1860 so it is quite possible that they would have distributed some muzzle loaders. I can't find anything about J Gebhard on Google. I suspect was a hardware store in Ft Wayne Indianna, but the original owner could have had his name engraved on the barrel.
That should be 'PRINCIPE-BILBAO' which refers to where it was made in Spain. PROCOMSA is an industry name associated with metal manufacturing, but I can find no reference to shotguns. In any event, importation into the US was not well-known although the 'Made in Spain' marking would indicate it was specifically marked for the US market. Value would be somewhere less than $100. sales@countrygunsmith.net