No, you are not required to hold a high school diploma (or its equivalent) in order to obtain an NYS real estate salesperson's license. You are only required to be at least 18 years old.
Yes, only an NYS real estate broker is required to be a U.S. citizen or permanent resident. Salespersons are not required to be a U.S. citizen or permanent resident; however, you must have at least a social security number.