The Knaak drilling first: The gun was made and proofed in Suhl post-1912. No, it cannot be considered an off-season arm, as it's rifle barrel is proofed for a cartridge considered a "serious big-game load" by some around WW1, even popular today for roe deer shooting. The markings 5.5mm bore diam., 52mm case length and 4 gramm copper jacket bullet show it to be a 5.6x52R aka .22 Savage High Power. A family relationship Knaak/Max Meffert is not known, but both gundealers were near neighbors in Berlin, Friedrichstrasse. In 1910 after a settlement M.Meffert's business was amalgamated into "Deutsche Waffenfabrik Georg Knaak", already owned by Max Meffert since 1908. Also in 1910 the company was bankrupt, but it continued under obscure ownership and management at least to 1941. Despite the designation Waffenfabrik = arms factory it is very doubtful if they ever actually made any guns, they were sort of international dealers in all kinds of arms , ammo and military equipment, so the drilling was probably made for export.
The Jung drilling in 7x57R and 16/75 was proofed in Zella-Mehlis October 1939, so it was made by the Z-M guntrade. There are 17 "Jung" listed in Suhl, 4 in Zella-Mehlis, 3 in Viernau, a village about 8km west of Zella-Mehlis, and 6 more elsewhere in Germany. The only August Jung was one of the Viernau Jungs, so he certainly was part of the Zella-Mehlis trade. In which way he was related to the other Jungs is unknown to me.