"Jaegerbuechse", "Jagdbuechse", or just "Buechse" for rifle. A "Jaeger" is the man who carries it.
"Flinte" is a bird gun, "Gewehr" is just generic "gun", "Stutzen" is a very short rifle, generally considered for use in heavy cover areas.
The average German rifle barrel length might be, oh, 28". They can be shorter, or longer. German smoothbore guns are just as long as anywhere else.
Rifles were probably used for target shooting as much as anything, hence the almost universal use of dual range sights and set triggers.
I don't know about the restrictions of hunting. There are a LOT of guns remaining, and there seems to have been at least one gunsmith in every little German hamlet. Too many for hunting to have been totally restricted. I have been told (I don't rember by whom) that large game tended to be restricted, but small game was not. I have yet to find anything really concrete in this area... :hmm: