When words are used together regularly, rules are formed about their use not for grammatical reasons, but because of the association. 'Black and white' appear in that order because of collocation; they are always in that order and to put them the other way around seems wrong. For the same reason we 'make a mistake' when we 'do a test'. The reason for using these verbs with these is that we always do; this is collocation
Black and white probably started as black on white - it is "down in black on white".
Make refers to making some thing whereas do refers to a process - the student didn't make the test, the teacher did, the student underwent a process, but made a mistake.