You're over-complicating this.
Forget about playing scales from different roots for the time being. Have you played around with constructing triads (the most basic chord) from the major scale?
Basic triads are formed by taking a root note, which for our purposes can be any note from the major scale, going up two notes on the scale to get the third, then going up another two notes to get the fifth.
In C major, the triads you get are:
C, E, G
D, F, A
E, G, B
F, A, C
G, B, D
A, C, E
B, D, F
All of those triads have a root, a third and a fifth. The root is the starting point, the third is the third note in the scale, starting from the root (eg. C, D, E = 1, 2, 3; D, E, F = 1, 2, 3) and the fifth is the fifth note counting from the root (eg. C, D, E, F, G = 1, 2, 3, 4, 5; D, E, F, G, A = 1, 2, 3, 4, 5).
Not all thirds and fifths are equal. If you count the number of half steps (frets) between C and E,for example, you'll get four. If you do the same for D and F, you'll only get three. That's the basic difference between an interval of a major third and a minor third.
Looking down the list of triads in C major, and concentrating only on the thirds, we find:
C, E = major third
D, F = minor third
E, G = minor third
F, A = major third
G, B = major third
A, C = minor third
B, D = minor third
If we were to do the same for the fifths, we find that all the fifths have a distance of seven semitones (frets) except for that of B to F which is six semitones. That's the difference between an interval of a perfect fifth and a diminished fifth.
C, G = perfect fifth
D, A = perfect fifth
E, B = perfect fifth
F, C = perfect fifth
G, D = perfect fifth
A, E = perfect fifth
B, F = diminished fifth
If we apply these intervals to the triads we made from the major scale, we find we have three different types of triad. One is made from a major third and a perfect fifth, one from a minor third and a perfect fifth, and one from a minor third and a diminished fifth. We call these major, minor and diminished triads:
I: C, E, G = major triad
ii: D, F, A = minor triad
iii: E, G, B = minor triad
IV: F, A, C = major triad
V: G, B, D = major triad
vi: A, C, E = minor triad
vii: B, D, F = diminished triad
The roman numerals are a convention for naming the chords that doesn't depend on key.
Usually, you'll see chords named like this:
I: C, E, G = C
ii: D, F, A = Dm
iii: E, G, B = Em
IV: F, A, C = F
V: G, B, D = G
vi: A, C, E = Am
vii: B, D, F = Bdim or Bo