The major scale is I, ii, iii, IV,V etc,

the chords that I know that would match up with that would be:
ex. Cmaj,Dmin,Emin etc.

My question is this. Can it also be: C6, Dmin6, Emin7, Fmaj9 etc.
Can it be any kind of chord as long as it coincides correctly with minor or major. I know the C6 is dominant how does this work.

That's correct your just adding color to the chords by using the notes of the major scale. C6 is C major chord with a added six of the scale not a dominant. A dominant chord contains a tritone. In the key of C that would be G7. The 2 notes F and B make the tritone.