Hi,
Looking at your pictures, I see little scratching on the cylinder, so it would seem that timing is pretty good, especially for the age of the gun.
If you get a good gunsmith to check and polish the inside. ( I mean the working parts, and verify their hardness ) you should have a good shooting gun.
Please keep a good supply of white grease on the cylinder pin while shooting to prevent unnecessary wear on the inner working parts.
As black powder residue builds up, it becomes harder, and harder to cock the hammer, resulting in greater wear on the hand that rotates the cylinder.
I have shot Pyrodex in these cap guns at it works well, IF the powder is new. You can shoot many, many shots in a day without binding, whereas real BP will force you to clean up after a few cylinders of shooting. If the hammer becomes difficult to pull back, clean the gun.
You can cause harm to the hand of the revolver with just a few shots.
I do not know if new Uberti parts fit exactly into your revolver. They should be close. If you can get to a place like Dixion's or Friendship, you should be able to get some spare parts, to keep your shooter going for many years.
Once again, I hopes this helps.
Oh, did I tell you, that I love black powder hand guns?
Fred