The 13/1 mark is for a standard bore diameter of .719". A 13/1 gun can go up to .728" before it is out of proof. It looks like there is a diamond proof mark as well but I cannot clearly see what that mark is. Those marks look consistent for Birmingham proofing between 1887 and 1896 or from 1896 to 1904 if the max load weight is added, for example "1 1/8 oz MAX". Unfortunately, we cannot see enough in the photos.

The forearm looks pretty old and worn to me, cracked as well.

In some of the photos the barrels look like they might be twist steel. Are my eyes decieving me?

Black powder gun means you will have very limited options for factory ammo. Reloading would be the way to go even for shot.

The sights are set up for ball. I question the originality of the rear sight because it appears to lack a registration mark to correspond with the mark on the rib just in front of it. But the registration mark on the rib does suggest there was another blade sight, perhaps a folding sight similar to those on Paradox guns. Folding sights are not robust and it is plausible that one broke and was replaced with a standing blade. I am speculating. The height and shape of the rib, especially in the rear, also suggest this was originally made for ball. No matter, if you are primarily interested in this as a ball gun the current sight, original or not, should work fine.

Your biggest concern should be regarding regulation. Will the gun regulate round balls? Will you be able to find a regulation load? If it can put two balls into 6" at 50 yards then you have a usable double gun. If it puts two round balls 18" apart at 50 yards you absolutely do not.