Is the money distributed by the manager as a bonus to employees — in exchange for using their private cars for office purposes — lawful or unlawful, knowing that this action violates the parent company's policy?

If what the manager did was an act of reward and income enhancement, then there is no harm in taking the money, even if it is outside the company's policy. This is because it benefits the work, and typically, the manager has the authority to make such a decision.