How are the two properties (the apartment building and the villa) divided according to the provisions of Islamic inheritance, and is it permissible for the sister to take all the gold and jewelry left by the mother based on her will, without it being subject to the Sharia division of inheritance, especially since the eldest son financially assisted his father in building the villa?

A will bequeathing gold and jewelry to a sister is not valid because she is an heir, unless the other heirs agree. The ruling on the money paid for building the villa depends on your intention: if it was a donation, you have no right to it. If it was a partnership in ownership, then you are entitled to what you paid, and you must prove that. The division of the inheritance is as follows: If the father died before the mother, the mother gets one-eighth, and the remainder goes to the children, with the male receiving the share of two females. If the mother died before the father, the father gets one-quarter, and the remainder goes to the children, with the male receiving the share of two females.