Why is the verb in third person singular when the subject is plural? Or is шесть человек considered a mass singular noun?
When the noun is used with a numeral, you can use either plural or singular verb.
Cmiiw i think люди refers to people in general without how many personnels specified.
I'm also confused by this - shouldn't the sentence be: "здесь живут шесть людей" ?
I think both should work here.
Yes, I guess so. «Шесть людей» sounds quite colloquial (and in general it sounds worse than «шесть человек»).
You cannot say шесть людей because люди are not countable. And Russian prefers a verb in a singular form when there is a number in subject. Здесь живёт шесть человек. Здесь их живёт шесть.
Челове́к is a strange noun that is normally not used in plural (the normal plural form is лю́ди ‘people’), so it doesn’t follow the usual rules.
Doesn't "man" refer to people without specifying gender as opposes to men?
It can, depending on the context. Usually it's applied this way in a more philosophical sense when speaking of humanity in general, as opposed to animals or gods.