Is what the father did, helping his married daughter by selling an apartment and furnishing another, and giving her his car, considered just? And if not, is it obligatory for him to pay his married daughter a sum of money?

Justice must be observed among children in giving gifts, and it is forbidden to favor some over others unless there is a legitimate reason, such as need or an excuse. As for maintenance (nafqa), it should be given according to the child's need, and equality is not required therein. So, if the car is something you genuinely need and you do not have the financial ability to purchase it, this falls under maintenance, and your father is not obligated to give your sister a similar car or its equivalent value. However, if you do not have an urgent need for it, or if you have enough to purchase it, then what your father gives you is a gift, and he must be just among his children by giving the female half of what he gives to the male.