Why doesn't red require the mau classifier?
"màu" does not act as a classifier, it just means colour. it is not necessary to add it, but from my very own perception, I see it as a way to contrast/underline that colour as opposed to others.
In this sentence could toi be used with same meaning? Also doesn't minh also mean ours?
it is more likely be used as the reflexive pronoun here, but true many VNmese use this to mean the intimate we/our.
Minh reflects back to the subject of the sentence...it can be me, you, they, him.