In the cases of a teacher or friend, those proper nouns would take the form of proper names, since they are people and people's names always begin with capital letters. And a person's title (like a rank in the military, job title/position, or a member of a royal family for example) always begins with a capital letter, so that too would be considered a proper name.
Geographic world locations (cities, states, countries, islands, continents, bodies of water, mountains, etc.) are all proper nouns and therefore begin with capital letters. Government locations (names of schools, capitol buildings, office towers, law firms) would also be written as proper nouns.
Basically, a proper noun or proper name refers to a specific individual thing or person in a certain category like those listed above, as opposed to a general categorical term of sorts.
I hope this helps!