(i)Too, an adverb*, is used at the end of a sentence or clause when it means 'also'.
(ii)I am/he is/you are, etc. too.
informal especially American English
used to emphasize that you disagree with what someone has said about someone or something
'You're not smart enough to use a computer.' 'I am (not smart enough to use a computer) too!'
*An adverb modifies another adverb, adjective but not a noun. So your first and second questions are no longer tenable.