major chord; maj. 3rd, min 3rd (A C# E)
minor chord; min 3rd, maj 3rd (A C E)
Diminished; min. 3rd, min 3rd (A C Eb)
There is no such thing as a major, minor, or diminished note, These terms apply to intervals that are created when you apply these notes against the chords. If you stay on the same note the interval will change every time a new chord is applied.
2nd question; You can play the chord tones in any order, it is still the same chord. The technical term for this is called an inversion (a chord with something other then the root as the lowest tone).
3rd question; Use your ear to determine when to apply the diatonic chord over the melody, there are no rules for this.
