What difficulty level (Normal/Hard/Maddening, Casual/Classic) is required for a speedrun to count?

Any is fine, most use Normal Classic as it is the fastest

No specific difficulty is required, although I'm guessing if you did maddening you could propose a separate category for it? But yeah do whatever you want, Normal/Classic is fastest (kill off your students in order to not have them ask questions/get in the way/learn skills.)