OP has little that can be done regarding diagnosis of any problem, meter function vs. shutter function vs aperture function issue...one can merely test and see if the resulting negatives have film density which is similar to another camera with known-good function...and if not providing results similar in exposure density, discontinue using the Leica Mini3!
One can point the lens at any area of uniform density, whether white or black or middle tone, and all three should result in middle density on film...that is what a meter does -- render what it sees to middle tone! If meter or shutter or aperture are not functioning properly, the result will not be 'middle tone' as captured on the film. Look at the film, not at prints, as the printing process by its nature would reduce shot-to-shot variances captured on film to the same final print density, if a single uniform tonal area is filling the frame...all properly functioning cameras should yield similar negatives, with similar density frames