Must the son return what the father paid him in exchange for his care, especially if the father paid it willingly and did not ask for its return during his lifetime?

What your father paid you as a gift is permissible, and you are not required to repay it after his death. The scholars have stated that it is permissible for a father to favor some of his children with a gift for a reason that necessitates it, such as your care for him and your filial piety towards him.