(a) That's wrong. The courts will give effect to limitation and exclusion of liability clauses to the extent that they are properly incorporated into the contract, and to the extent that their meaning is clear. But the courts have also said that any such clauses are obviously intended to operate within the context (or parameters) of the agreement, and do not extend to circumstances that fall outside of the 'four corners' of the agreement.
In the example, if the coat had been damaged during cleaning, A would not be liable. But because it was damaged while A was doing something he was not authorised to do under the contract, his liability is not excluded.