Boy, that is an oldie. The other guys told you right. It is a drilling and comes from the German word "drei" for three. "Drei" is pronounced like "dry" but, drilling is pronounced as the English word. It is on a Lefaucheux action, developed by the Frenchman Casimir Lefaucheux in the 1830's. They were originally pin fire and as cartridges evolved into what we know today, the action also evolved from pinfire to center fire. I would call yours a "rail" drilling as the rifle barrel is in a top rail. There is several barrel configurations of drillings and you can look them up.
My Lefaucheux double rifle does not have a barrel attachment the same as yours. However, I think you tried to disassemble it incorrectly. Put it all back together with the action closed. Then open the action. When the barrels reach their limit of travel, then I believe is when you detach them from the forearm and they should lift off. That's the way mine works but the barrels are attached with a barrel key, similar to a Hawken type muzzleloader. I might be crazy too but I think that's how they work. There might not be much for proof marks as Germany did not have a proof law until 1891-93 and I'm confident your drilling pre-dates that. I think that drilling was made not long after Germany became the country we are familiar with in 1871.
J.U. Banzinger might be the maker but it is more likely he was just the retailer. The ST GALLEN has me bumfuzzled. There is thousands of towns in Germany I'm ignorant of and probably hundreds that ceased to exist after WWII. That's what happened to the town in East Prussia my family came from, it's gone. Anyway, I don't know if the ST stands for "strasse" for "street" or like the abbreviation St. Seems either is possible but that is beyond my German language knowledge.
The shotgun barrels are more than likely 16 bore. 16 ruled the roost in Germany until after WWII. They're also probably only 2 1/2 in. chambers. The rifle? I don't have a clue with the description, "looks about 45 caliber." Even if we had the caliber it's hardly possible to know the cartridge without a chamber cast and, given the age, maybe not possible WITH a chamber cast and, being in the rail, it can't possibly be a very powerful cartridge anyway. Besides, those were black powder days so it's unlikely to be much more than a small game cartridge.
Whatever the truth of the matter is, it's an interesting old piece. You just don't see many rail drillings.