Try Blue Book of Gun Values
Check the receiver and barrels.
open gun where the barrels latchs,the model numbers will be right there.
It's a Belgian gun, the ELG is a Belgian proofmark.
Open the action. It is stamped on the water table, which is the flat part of the frame where the barrels sit. sales@countrygunsmith.net
Try the gunbroker.com, or do a google search on the specific barrel you need. Mid West Guns also carries Browning Barrels.
Try your library.
there are many avenues to find barrels for A5's. Try the "gunbroker.com" firearm barrel section. A5 barrels are sold there all the time.
You can try Hasting's. They make after market barrels.
Information on this weapon can be found at any reputable gun dealer. And any bookstore will have catalogs on old or new firearms.
Most old Damascus barrels cannot hold the pressures of modern smokeless loads. I doubt that you will find any black powder loads for that type of barrel. Hang it on the wall and admire it.
Will be hard to find, and expensive. Do an internet search for Corson's Barrels.
It depends on the Manufacturer, model, and series. I don't see why you couldn't change the barrel size if you find the barrels the same as the 20 inch models. A gunsmith should verify that the headspace is correct with the replacement barrel. The barrel length isn't the concern - it is the fit at the breech that might be off. If there is too much clearance between the end of the barrel and the standing breech, you might be unpleasantly suprised.