Must the son, who lives in one of the free apartments, pay a portion of the rent to his unmarried sister, who is still dependent on the father, as well as to his married sister?

One must differentiate between nafaqah (definition) (financial support/maintenance) and atiyyah (gift). The nafaqah that a father spends on his children varies according to their needs, and he is not obligated to equalize it. Rather, he gives each child what they need and what is appropriate for them, such as expenses for studies, marriage, housing, or a car. As for atiyyah (gifts) that exceed nafaqah, equality among children is obligatory, and the male is given a share equal to that of two females. It is not permissible to prefer one child over others.

Based on this, if a father permits his married son to live in one of the apartments without transferring ownership, there is no harm in that as long as the son is in need. The father is not obligated to give anything to his other children, nor is he obligated to give the remaining children anything as long as they are not in need of housing. However, if the son is not in need of housing and allowing him to utilize the apartment for free is considered a gift (atiyyah), then justice requires that the father give the rest of his children an amount equivalent to the apartment's rent, or the son pays the rent, or he gives his siblings their share of the rent. If the father wishes to transfer ownership of the apartments to his children, he is obligated to be just among them and make the share of the male double that of the female.