Do we need to make reservations or can we just come and pay for the tour at the door?

You can do both, but reservation is preferred as this place gets crowded

You may buy tickets online or upon arrival. Stan Hywet is open Tues.-Sun. 10am -6pm. Last entry at 4:30 pm. The Manor House opens for tours at 11 am. Find more info, buy tickets at stanhywet.org

You can do either. They have a set amount of slots per hour, so you can always check online to see if they have plenty of available slots, then pay when you arrive if you like.