Your pistol exhibits what is typically referred to as high-point holster wear, i.e. wear around the muzzle, trigger plate "island" and some other areas, normal for military Mauser Lugers of this time period. Such wear is consistent with your grandfather's story of the pistol's history, and tends to corroborate the story in that it is evidence the pistol has not been refinished.
Sometime in 1937 Mauser switched to salt bluing and stopped strawing parts; 1937 pistols that preceded this change like yours are sometimes referred to as "1937 first variation" in a nod to this finishing change and are, all other things being equal, slightly more valuable than the later all-blued pistols. Further comments on proof marks, magazines would require clearer photos including photos of the magazine bottoms. Quality, type, numbering of magazines is an important part of assessing any Luger.