From my experience the "ч" and "щ" have two different sounds. "мужчина" should sound like "moo-she-na" while "жеищина" should sound like "jze-chin-nah". The "ч" sound is like the CH in cheer and requires a light tongue, the "щ" is like the CH in chin and requires a heavy tongue in the back of the mouth.
If you know how to pronounce separate sounds then "мужчина" is pronounced as "мущина" and "женщина" => "женьщина". Why are they spelled differently? There is basis of the word "муж" in "мужчина". "чин" is a suffix. I believe that some time ago it was pronounced the same way it is written at least in some territories but due to some simplifications it was modified. Even for me, native speaker, it is weird that such a popular words are so complex and long.
There is almost no words with "жч" combination and all except "мужчина" are extremely rare. It is pronounced as "щ". The exceptions are words with prefix "меж-" (inter-) like "межчелюстной" (intermaxillary). Here "ж" and "ч" are pronounced separately as they are but I doubt you need all these rare words. Just remember how to pronounce "мужчина".
Multiple issues (for me this was in practice where I only heard the audio)...
From that pronunciation/intonation (the current male voice), how was I supposed to understand it's a question? Is there some dead giveaway or something like... it has to be a question if it's constructed like that?
I'm sure "Is this a man[?]" is equally correct, no? Here, the 'this' or 'that' is not in a literal sense indicating a particular man, it's purely an expression (in English). One more thing I'm not so very sure about but definitely crossed my mind is that the Russian sentence could have many more meanings depending on context and intonation (is it a question or is it not! What if the question mark wasn't there? or you couldn't clearly hear the raising stress on MUzhchina? where the stress BTW should be IMO, on the first syllable. Please do correct me if mistaken).
What do you guys think?