The sentence that is correctly hyphenated is "The beauty of Mount Fuji's near-perfect cone shape has enchanted people for centuries."
Near-perfect is correctly hyphenated because in this context it is a compound modifier, it modifies Mount Fuji's appearance.
The words in the brackets are telling the actors what to physically do, meaning it would be a stage direction.
It isn't dialogue because that is a conversation between two people.
It isn't dialect because that is how a person speaks. There is no speaking in the brackets.
It isn't narration because it isn't spoken allowed for the audience.
It isn't a description because that is too broad a term more often used for emotions.
