Is there a certain amount of hours a salaried person has to work in one day that they will be paid for the entire day even if they leave early? For instance if a salaried person works 8:30 to 1:00 with no break do they get paid for the full 8 hours of the day or do they need to take personal paid time off?

A salaried employee should be paid for each day the show up. However, if they leave early company policy can require that they use sick or personal time for it.