My flight left at dawn. I left the car in perfect condition in the car park of the rental company. Yet the rental company has charged me repair costs. Can they do this?

As for the problem with the clutch, the rental company must be able to prove that there is damage, and that this was caused during the rental period. In practice, car rental companies will not hesitate to charge you for any damage they have unilaterally observed. You should therefore take pictures of the car with an indication of the date when leaving it in the car park.