Oh, is that a valid way of grouping determined nouns instead of saying a nők és a férfiak?
Is "férfiak" an irregular plural? It doesn't seem to follow vowel harmony.
It's even worse, it also behaves like an adjective. ...Okay, that doesn't really make a difference, save for using -ak over -ok for the plural.
To answer your question: yes, it's an odd one. You will find some words that have a stray é in them but otherwise follow back vowel harmony. For instance acél (steel, acélja - his steel) or béka (frog, a békának - for the frog). There seems to have been a different back vowel sound in olden times that has been since replaced by é.
There are two nouns, that I know of, that have strictly front vowels only but still attract back-vowel suffixes, both of them with the vowel é: cél (célok, célom, célod) = "target, goal" & héj (héjak, héjam, héjad) = "shell, peel (of a fruit)"
The explanation is probably a vowel shift from the close vowel í... or a back vowel.
The English here is grammatical. But I think most English speakers in most cases would say 'the men and women' rather than the 'women and men' -- perhaps out of custom. Anyway, my question is: Does Hungarian etiquette (or perhaps euphony) favor mentioning the women first, or doesn't it matter much?
It depends. Usually in a sentence where multiple types are mentioned (women and men, cars and bikes) the ones with the larger number are mentioned first. If the count is the same, then the speaker can decide.