(a) That's correct. In this example, it is obvious on the known facts that B's promise to obtain the permits was of fundamental importance to A.
This conclusion is justified because it is clear from the known facts that, if B had not made that particular promise, A would not have entered into the contract to lease the building, and B must have been aware that this was the case.
The courts often refer to the more important terms in a contract as 'conditions'. In the present case, B's promise to obtain the permits is a condition.
It is important to determine whether or not a term is a condition or not because this affects the remedies available in the event of a breach of that term.