(a) That's right. It is a universal term of all contracts that the parties cooperate in the performance of the agreement so that both parties get the expected benefit of the contract. In Alcatel Australia Ltd v Scarcella (1998) 44 NSWLR 349, Sheller JA made a clear statement recognising the existence of such a duty. He said (at 368):
"The common law imposes a duty on the parties to a contract to cooperate in achieving the objects of the contract."
Similar statements have been made in decisions of the High Court of Australia.
Although the agreement in the example gives B a right to say whether particular times would be inconvenient for an inspection, a duty of cooperation would oblige B to act reasonably in allowing an inspection to take place. This is necessary to enable A to have the benefit of the contract.