The difference between East Egg and West Egg is that East Egg is largely populated by those from "old money," while West Egg is populated by those with "new money." Tom and Daisy Buchanan are from old money because their families have been wealthy for generations.
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.
You can acheive the appropriate writing style for your writing essay by using combination writing, or explanitory writing.