1. Either: any one of two. Each of two (A garden with a fence on either side) Either…or: introducing two choices (Either you come or I go)
Neither: not the one, nor the other. Neither proposal is acceptable. It is normally followed by a singular verb. Neither of them is coming. However, in informal usage the plural is common: Neither of them are coming
Both: the two.

2. So, too, neither, not either, but
And + so+ be/do + subject: affirmative
Amy is a twin and so is Sue
Amy likes dogs and so does Sue
And+ subject+ be/do + too: affirmative
Amy is a twin and Sue is too
Amy likes dogs and Sue does too
And + neither +be/do + subject: negative
Amy isn’t tall and neither is Sue
Amy doesn’t like cats and neither does Sue
And + subject + aux + not either: negative
Amy doesn’t like cats Sue doesn’t either
But + subject + be/ do/aux + not: contrast
Amy is outgoing but Sue isn’t
Subject + do + not +but+ subject + do
Amy doesn’t drive but Sue does