Is it permissible for me to take the amount allocated to me from the sale of my father's house to my brother as a gift or an endowment, after my father has registered the house in my brother's name in exchange for a sum of money to be distributed among family members according to a specific division, and is this division in accordance with Sharia?

As long as the father's sale of his house to one of his sons is for a price paid by the son to the father, then it is a valid sale. The father may dispose of the proceeds from his house as he wishes. However, whatever he bestows upon his children must be distributed equally among them, males and females, unless there is a reason that necessitates preferential treatment. Some scholars are of the opinion that justice is achieved by giving the male twice the share of the female. If all adult children agree to the preferential treatment, then there is no harm in that.