My dictionary lists "
both" as a pronoun, conjunction, or adjective. It is not an adverb.
Each is an adverb is only one sense - meaning apiece. In all other definitions, it is a pronoun or adjective. Example:
The bananas cost 50 cents each.
All has many more uses. It can be a pronoun: "all of us are coming", an adjective (in all cases), and adverb, meaning "completely". As an adverb, it usually modifies an adjective, describing degree or extent.
I am all tuckered out.
I am all alone today.
We are all finished with the work.
When you are all done, go back to the reception area.
As a pronoun, it can be a subject, object of a preposition, etc.
All of the men are coming to the party, but not all the women.
He gave a prize to all who entered the contest.
Not all will be happy with the settlement.