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
A barrel maker is a person that has a skill for making wooden barrels. Another name for a barrel maker is a cooper.
If you google that name you will find several persons of that name. So there is no single answer.
A bayonet is the name of a knife attached to the barrel of a rifle.
It's just called a barrel.
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.
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.
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