How is inheritance divided in the mentioned cases, and why does the husband inherit more than the wife, with mention of the Shar'i (Islamic legal) proof?

If the heirs are limited to those mentioned, the inheritances are distributed as follows:

1. Three daughters and two parents: The daughters receive two-thirds, and each parent receives one-sixth. 2. One daughter and two parents: The daughter receives half, each parent receives one-sixth, and the remainder goes to the father by ta'sib (agnatic inheritance). 3. Nine daughters: They receive two-thirds, and the remainder goes to the nearest male agnate. If there is none, the remainder is returned to the daughters. 4. Two parents only: The mother receives one-third, and the remainder goes to the father. 5. A wife and a daughter: The wife receives one-eighth, the daughter receives half, and the remainder goes to the nearest male agnate. If there is none, the remainder is returned to the daughter, but not to the wife. 6. Four wives and two parents: The wives receive one-fourth, divided equally among them. The mother receives one-third of the remainder, and the father receives two-thirds of the remainder.

As for the question "Why is the husband entitled...?", it is not relevant for a Muslim who submits to the judgment of Allah and believes that Allah is the owner of everything, and that the division is just. The general rule is that a male's share is twice that of a female, with some exceptions. For an atheist, financial burdens are often associated with the male, hence his share is twice that of the female. There are cases where a woman inherits and a man is disinherited, such as a full sister who has a prescribed share, while a full brother inherits by ta'sib. A son's daughter may inherit while a son's son does not inherit in the same situation.