Terry, this may help clear up a few details (quotes from your opening post):
If I capo up to fret 3, the A major chord shape gives C, E, G, thus a C major chord. True.
Similarly, if I capo up to fret 2 I would get a B minor chord.Not with an A major chord shape--it would be a B major chord. An A minor chord shape with the capo at the 2nd fret will give a B minor chord.
But if I capo to fret 1, the A chord shape gives me D, F, Asharp - is this a proper chord?Call the A-sharp a B-flat (same note, different name), and you can see it's a B-flat major chord.
And fret 4 would give me Dflat, F, Asharp - what on earth can that be!Actually, that would be D-flat, F, and A-flat--a D-flat major chord (or if you prefer, call the notes C-sharp, F, and G-sharp and the chord a C-sharp major).