So, I find this funny:
If "lady" is « Madame » (ma + dame)
Then "ladies" is literally pluralizing it (ma in plural is "mes", it's a possesive), it becomes « mesdames »
But, I'm not sure if there's such word as « messieurs »
You're correct, just as the plural of madame is mesdames, the plural of monsieur is messieurs.
There is indeed such a word as messieurs -- it's the plural of monsieur !
The difference is definitely there in the audio. 'Madame' is pronounced /ma.dam/ and 'mesdames' is pronounced /me.dam/. It's just like the difference between 'ma' and 'mes'.
For 'Bonjour Messieurs' I wrote 'Hello sirs' and got marked wrong and told the correct answer was 'Hello men', so for this one I wrote 'Hello women' and get told the correct answer is 'Hello ladies'.
What is going on?
"Good morning, ladies!" doesn't sound nearly as formal as "Bonjour Mesdames!"