Is the division proposed by the father to the children concerning the apartment owned by the eldest son legitimate, and what should the eldest son do if he does not possess the amounts required of him to fulfill this division, knowing that the apartment was expected to be his?

Perpetual leasing is not Islamically permissible, even if the law allows it. All earnings and benefits derived by the lessee from a perpetually leased property are Haram (definition) (forbidden).

Therefore, it is not permissible to force the homeowner to sell the apartment at an unfairly low price. Rather, the apartment must be returned to him, or the remainder of its true price must be paid, or it must be leased from him with his consent at a fair market price for a specified period.

If you wish to purchase the apartment from its owner at its true price or with his willing consent, you may do so. If you jointly purchase it from the property owner at its true price, then each of you will have ownership in the apartment proportional to the amount you actually paid of that price. What you previously paid to your brother and sister is a gift that cannot be revoked, unless there was an agreement that it was a debt or part of the apartment's price, or if you intended it as a loan. In that case, it will be accounted for in your ownership of the apartment to that extent, if they agree to it. They also have the right to return what they took from you and retain their share of the apartment according to the contract.