Question: Is there a night train that goes from Mashad to Shiraz? I cannot seem to find any information or flying is the only way.

Answer: The train between Mashad and Shiraz has not been inaugurated yet. You can travel Mashhad to Isfahan on a train and on a bus or flight travel from Isfahan to Shiraz.
For train booking you can check: http://www.uppersia.com/Iran-transport-services/iran-train-ticket-booking-service.html

Check the cheapest Iran tours at http://www.uppersia.com/Iran-tours