your first question:
the major chord is built from the 1,3,5 degrees of the major scale, the minor chord is built from the same degrees but of the minor scale, where the 3rd degree is 0.5 tones lower than in the major scale.
the diminshed is based on the locrian mode, and built from the 1,3,5 degrees of the locrian mode, but the 3 degree of it is also half tone lower than in major chord, and the 5th degree is lower as well.
now if you will build the chord in 3,1,5 mode, or 5,3,1
that will be an inversion, so basicly you still have the same chord.