About the possible cartridge.
Austro-Hungarian or Austrian .50 caliber hunting rifle cartridges of the late 19th century are mostly variations of the .500 Express. The shortest version I'm aware of is 12.7x60R. As the case of the present rifle is only about 40 mm long, we should probably look elsewhere.
An older group of cartridges was based on the gauge system. Common hunting rifle cartridges were 24 gauge or 28 gauge, with about 40 mm cases. If we look for a .50 cal. cartridge in the (Austro-Hungarian) gauge system, the nearest would be 38 gauge or 12.6 mm. So this rifle cartridge could be 38 gauge (40 mm case), or in modern metric gun language 12.6x40R.
Kind regards,
Jani
