Usually אדם or בן אדם is translated as "human" but "man" is acceptable too. Also, הוא איש is he is a man. In modern Hebrew "person=human=man" isn't divided distinctly between איש / בן אדם/ אדם / גבר

It's kind of correct, but requires a certaun context. אדם is more correctly translated as "person", even though in Hebrew this is also a masculine noun and not neutral as in English. 1