"Nous sommes de vieux amis." I think it should be "Nous sommes des vieux amis."? Or is it because that "des" become "de" when there's an adjective after it?
Yes, that is the reason.
why is incorrect to put "nous sommes de vieux amies"
vieux is masculine
de vieilles amies is feminine
Why is the 'de' necessary?
singular: un ami
plural: des amis
in front of an adjective, "des" becomes "de"