Is common noun a proper noun?

Answer 1

No. Proper nouns are specific items. That is, not just any [common noun] but a particular example of [common noun]. "Person" is not a proper noun, but the name of a specific person is a proper noun.

If the phrase "a [noun]" is a reasonable one to use in a sentence, then it's probably not a proper noun. "A door" makes sense, so "door" is not a proper noun. "A pen" makes sense, so "pen" is not a proper noun. "A George Washington" seems a bit odd except in very specific sentences where you really mean something along the lines of "a person like George Washington", so "George Washington" is a proper noun.