I think we need photos of the action and barrel flats, (in focus), so we can work out what's what. The caliber should be shown something like 8/57mm. I can't see it being the 8x56 Hungarian Mannlicher as this was mostly a military round, in fact, I had one for the Steyr M.1895. I agree that Kruppscher Lauf or the like is probably the maker of the barrels, and the Krupp factory made them for anyone.

You'll also need to consider that many of the German 8mm cartridges were for .318" diameter bullets, not the "normal" .323", so you might need to reload. The good news is that none of these things is insurmountable and components are available. I shoot an 8x57JR Drilling with .318" bullets and it's quite accurate and straight forward to load for, just don't use ordinary 8x57 rimless maximum load data for a rimmed cartridge. The pre-war Drilling is usually chambered for rimmed cases because of it's weak extraction, but post war Drillings made for American markets may be chambered for rimless and, if so, you should see small, spring-loaded pins in the extractor that snaps into the case extractor groove.

The selector that erects the rifle sight has been around since at least 1900, so this doesn't tell us much about age excepting that, as you say, it's a neat feature. It also tells you, (unless you have a scope), that you've selected the rifle when you sight down the barrel rib. So you're less likely to shoot that rabbit with an 8mm when you had a shotgun blast in mind.

The pre-war 16 gauge used to be 2,1/2" (or 65mm)length and, again, these short shells are available, but not at every gun shop all the time. You can load them in an ordinary MEC loader, but you need a cheap spacer and you'll need to trim the cases and use appropriate data and wads. They carry about 1 oz and I dropped a swan with one that fell of the sky like it was electrocuted. If it's a post-war gun and you can see a 16/70 among the proof marks on the barrel flats, you probably have a 2,3/4" chamber. The 65mm chambers were usually not marked. A gunsmith can also measure the chambers and a good one can measure the lands and grooves of the rifle as well.

Drillings are neat guns, but probably not for everyone. But if you can shoot fur and feathers on the same hunt, grab it. Check the ribs (above and below, use a magnifying glass) for fine gaps where they connect with the barrel and then, hold it suspended by the hook, (without foreend) and, if the barrel lightly tapped rings true, you should have a good one.