The word "family" in the sentence is used as a noun. Words that fall under this category are used to refer to either, persons, things, happenings, events, place, etc. The word is derived from the Latin word "nomen" which means name.
B. The sentence that has an error in usage is the following one: Sometimes being a man simply means helping others bare their difficult burdens. The word "bare" in this sentence should be the word "bear" which means "to help endure or carry."
