(a) That's wrong. Although the courts will enforce exclusion and limitation clauses, they are reluctant to give them any more effect than is necessary. There has developed a judicial policy of interpreting such clauses strictly, and in the case of any ambiguity or doubt, to interpret them against the interests of the person who stands to gain from the exclusion. This is called interpretation 'contra proferentem'.
In this case, the court will see that the clause in question limits liability for breach of conditions in the contract. But the term that has been breached is a warranty, not a condition. Strictly interpreted, the limitation clause does not apply to the breach in question, and does not limit B's claim for damages.