What is the legal share of the heirs, what is the ruling on the deceased's will, what is the ruling on a father selling his property to the deceased mother, does the sister from the father's side inherit from the deceased mother, and how can injustice be removed from the father if it exists?

The question contains much ambiguity, but in short, it can be said:

Firstly: If the father's sale of his properties to his wife was a real sale at market value, it is valid even if it occurred during his death illness. However, if it was a nominal sale, it is considered a gift, and if it occurred during a perilous illness, it is a bequest to an heir that is not enforceable unless the other heirs consent.

Secondly: The mother's bequest of all her possessions to her granddaughter is only valid within the limits of one-third. Any amount exceeding one-third requires the consent of the heirs.

Thirdly: The mother's claim that she bought the land and built upon it, despite it being registered in the father's name, requires proof. Otherwise, the default is that both the land and the building belong to the father. The matter should be presented to the Sharia court or to scholars for all parties to be heard.