What role did Clarisse, Old Woman, Beatty, and Faber play in Montag's life in reeducating him?

Clarisse inspires Montag to examine his own life. Montag merely exists, Clarisse asks if he is happy. Montag discovers that he doesn't really know what happiness is. Clarisse gets him to examine what is real and what is not. The old woman shows Montag a type of courage he had not seen. She is willing to die for ideas, the ideas found in books. Beattty's role is rather complex. He acts as both an antagonist to Montag as well as a character foil. Montag understands how sick society is through Beatty's intelligence and pain. Faber is a mentor figure of sorts. He explains the mentality behind society and how it works.