The Parker Bros. company was in business beginning in 1866, but cartridge guns were already on the market in big numbers, and I still have a hard time believing that they made any percussion guns. I check an older copy of the Blue Book of gun values, and found no mention or percussion shotguns. Parker was bought out by Remington in the early 1930s, which marketed the guns until after WWII. Remington then dropped the Parker hame. There was a production of " replica " Parker shotguns by another company recently, but other than pictures I have never seen one of them in a gun show. They might be in a bigger show, but not the ones I have attended. All those replica guns were the break open breechloading internal hammer variety guns.
I would recommend taking the forestock off the barrels, and checking the bottom for proof marks. Use a piece of paper and make a rubbing with a pencil if there is corrosion or anything else that makes it difficult to distinguish letters and numbers. If you googel Parker Brother's shotguns, you can find sites that give you all the proof marks, dates of manufacturer, model designations codes, etc. for Parker Shotguns. If you still aren't sure what you have, list the details you do have here and someone will help you out.
As for shooting damascus barrels, if they are in good condition they are actually capable of handling more pressure than modern steel barrels. There is an article on this subject many years back now in the Double Gun Journal. I am sure a call or email to the publishers will get you a citation to the article and some direction as to how to get a copy of it.
On Damascus barrels that are not in good shape, liners can be made. A friend inherited an L.C. Smith hammer, damascus gun, that was badly corroded. He paid a skilled gunsmith to cut the barrels off in front of the chamber, bore out the chambers, and then fit new barrels as a liner to the 4 inch chamber section. The fit is so good you only see a very narrow line where the two edges meet, and it looks like a part of the decorative design of the barrel set to the uninformed. I believe the liner was held in place with an industrial grade epoxy. He refinished the stock, which was not particularly good wood, and has shot the gun for more than 15 years now, that i know. I think its too muzzle heavy, but to each his own. The barrels are choked modified and full, and there are separate triggers for each barrel and hammer. He is left with a damascus pattern on the action, and plain steel for the rest of the gun. If this were to be a restoration for sale, it might be worth having someone do a damscus-style design in the finish of the new barrels. But this is a family heirloom, that will be passed down to one of his sones, and it is not for sale. If it were a premium grade gun, he would spend the money to have a better piece of wood used to stock the shotgun. But, this gun was used to feed the family, and it was a no frills piece when his grandfather bought it and used it. Some things are best left unchanged.
Today, there are a couple of gunsmiths that can bore out the damascus barrels and put liners in them, so that you keep the damascus finish on the outside and have modern steel on the inside. Its expensive, but it can be done.
