Is "The happy men" an acceptable translation?
No, that would be הגברים השמחים.
It's all in the article!
This article agreement is also found in Arabic, another Semitic language:
al-bait kabiir. 'The house is big.'
al-bait al-kabiir 'the big house'
What is the origin of גבר? In Biblical Hebrew man and woman are איש and אשה. Pronounced (ish and ishshah) they seem clearly related, but in Modern Hebrew the word for man has entirely different consonants. Is איש ever used?
Is there a virtually silent 'a' sound between ש and מ, like in the word 'sameach', or is it not there at all in שמח'ם?
שמחים is always pronounced as 'smekhim'. The 'a' sound is reduced.
Is the correct pronunciation of "הגברים" ha gevarim or hag varim?
More like the second option, but it should sound like one word "hag' varim"