Am I allowed to drive a car designated for my father from his work, knowing that it belongs to the company and my father is permitted to use it however he wishes, without selling or renting it?

It is permissible for an employee to use the company car for personal purposes and to lend it to others if the responsible authority permits him to do so. Otherwise, it is not permissible, due to the saying of the Prophet, peace be upon him: "Muslims are bound by their conditions," and the saying of Allah the Almighty: {O you who have believed, fulfill [all] contracts}.