semitones. 0 is your major key tonic, the major scale is:

0    2    4    5    7    9    11    0'
M   m   m   M    M   m  dim

0' being an octave higher than 0.

you listed the triads correctly.

triads are created by selecting a pitch (root), then a pitch 2 scale degrees higher (3rd), then another pitch 2 scale degrees higher further (5th).

a minor triad is root, plus the pitch 3 semitones higher, plus the pitch a further 4 semitones higher.

a major triad is root, plus the pitch 4 semitones higher, plus the pitch a further 3 semitones higher.

a diminished triad is the root, plus the pitch 3 semitones higher, plus the pitch a further 3 semitones higher.

[0]    2   [ 4]    5    [7]    9    11    0'    
 r            3rd         5th 
       4st           3st

here's the first triad. it's clearly major: root to 3rd is 4 semitones (4st), and 3rd to 5th is 3 semitones.

the rest are done identically.

Depending on where you start do you pretty much have most of the modes here

it's not where you start, unless you're playing a scale. playing music the mode is which pitch is your tonic, i.e. home note. generally you'd end on the tonic, and the music should feel as if it's come to rest (it shouldn't sound incomplete). usually you start on the tonic too, though there are exceptions.

and you don't have 'pretty much all the modes', you have them all.

the minor mode in your description is 6, not 3

i.e.

 0       2      4       5       7       9     11     0'
 Maj   Dor   Phry  Lyd    Mix   min    Lo

all music is essentially in major or minor.

guitarists seem to obsess over modes, but temporary departures from you key centre to a new region aren't viewed as modal playing, as almost always these departures don't construct phrases that come to rest in the new region, rather you depart away again, and when you finally do come to rest it's back in the major or minor.