2. (a) That's wrong. A principal must compensate the agent for liabilities and losses incurred, but only if the agent was acting within the authority given, lawfully and not negligently.

In this case, it would seem that B was driving carelessly in trying to squeeze through a gate that was not fully open. Because the damage to A's car is due to B's own negligence, he would not be entitled to recover the cost of the repairs from A.