No, that order sounds unnatural here. Here are some other examples.And shouldn't number three be What hair color... instead?
No. It's possible with many nouns, e.g. "What colour shirt should I wear?"Hi again,
I've just read that you say eye colo(u)r (that is, the word order a non-native like myself would expect), does the word order color+noun (meaning color de + sustantivo) only apply in connection with the noun hair?