Possible Clues:

• Something hard to explain
• My better half is taken in by extremely shady enigmatic type
• The writer's tale given a new middle section -- detective story?
• Can't figure out why my tyres burst
• My story with Oxford’s head ousted by Eton’s head — crime novel?
• See 13 Across
• See 16 Down
• The Chester ____ Plays are a medieval drama series revived in 1951, and will next be performed in June and July 2023
• Something not understood
• It passes all understanding