Re: German derringer
Those guns were made by the ton and are the equivalent of our low cost revolvers of the c. 1900 period. They generally bring $75 or so as curios, but if the engraving is nice (the pictures are so bad I can't tell what it is like), and the gun is functional and in good shape otherwise, the value could go to $200 or so.
Similar guns shown in the 1911 Adolf Frank (Germany) catalog sold for 10-18 marks, or about $2.50-$4.50 at the time. (Unengraved ones went for 5 to 6 marks, and a Colt Model 1878 was 118 marks or $29.50.)
I wonder if the gun could be the British .320, a common caliber in those guns, rather than .38 or 9mm caliber, which would be unusual.