Taking your questions one at a time.
"How can I distinguish the earlier Navy model from the [1860] Army model?"
The Navy will have a 7 1/2" octagon barrel and will be .36 caliber. The 1860 Army was .44 caliber with an 8" round barrel (although a very few were made with a 7 1/2" round barrel).
"How can I determine when and where this revolver with its serial number was manufactured?"
It was made in 1863 by Colt in Hartford, Conn.
"How long were revolvers such as this in general use in the U.S.?"
Colt discontinued their percussion revolvers in 1873, but they remained in use for many years after that. However I would GUESS that by the 1880's cartridge revolvers were gaining considerable ground.
"Would caps and balls for it have been readily available after 1900?"
Yes.
John