They are still being made.
The use of damascus barrels on guns began to decrease pretty rapidly after 1900, although they were still fairly common up until the start of WWI. If you have a breech loading gun with damascus barrels it will probably date from 1875 - 1910. Most damascus barrels on U.S. guns seem to have actually made in Belgium. There is a lot of debate as to whether any damascus barrels for shotguns were actually made in the U.S. It seems likely there may have been small numbers produced in the U.S. However, Belgium had a large gunmaking trade at the time, with a lot of barrel makers specializing in damascus barrels, so it was generallly cheaper to import them than to make them.
No.
Some did, but not all.
The time of the First World War pretty much ended the importation of Damascus barrels. US manufacture started petering out in the 1890's.
About $100 or so. The damascus/twist steel barrels are generally considered unsafe to shoot with modern ammunition.
no . riverside was mainly produced after 1914, using fluid steel barrels.
There was no specific date, you could order them either way for many years, damascus was usually the more expensive of the two. I'm quite sure though that any Lefevers made by Ithaca had "steel" barrels (although there probably were some Lefever made guns left over and sold by Ithaca). Ithaca acquired Lefever something around 1916.
50-150 USD
DO NOT FIRE WITH MODERN AMMO!!!!!!!!!!!!!!! MUST be checked out by a gunsmith.
no not all twist barrells
I'm not sure exactly what you're asking here. Generally a shotgun with Damascus barrels (those showing a spiral pattern on the outside, since they were made from spiralling layers of metal) will have been made for black powder only. In their time, fine Damascus barrels were considered a superior option, but caution should be exercised shooting such guns now, and definitely only black powder should be used. If in doubt, get the gun checked by a qualified gunsmith.
We cant find one for you here. Browning Arms Co never made a shotgun with damascus barrels as far as we know. Its possible that a gun was made with those barrels built on one of Brownings patents.