ok, dont have so much time now but looks very fine. krupp laufstahl, nitro proof for the shootgun barrels- strong like......kruppstahl
7,7-57 and Mod.88 8 M.must be 8x57 IR Witten Excelsior steel!!!
shotgun barrel seems to be Teschner/Collath No.4, it is common practise to use the shotgun bore that fits

lets check the barrel diameter from competent gunsmith

looks like a best gun from germany