First, I should mention that although this is the Muzzleloading Forum, discussions about breech loading guns is permitted as long as the gun uses a separate percussion cap which is not part of a cartridge. This was done because forms of breechloading guns were made dating to the flintlock era. The Ferguson Rifle comes to mind.
According to Flayderman's Guide, 9th ed., the gun shown in the first set of photos is a Jenks Carbine.
A total of about 4250 of them were made. They were .54 caliber.
It should have a 24 1/4" long barrel if it hasn't been altered.
Jenks rifles were also made with a 35" long barrel in .54 caliber.
According to Flayderman's Guide, the carbine and rifle were the only Mule Ear (sidehammer ) type guns officially accepted by the U.S. armed forces.