Is the amount of money taken by the father from his deceased wife considered a debt upon him, and is it permissible for the son to pay it to the heirs from his own money with the intention of absolving his father, and should the amount be paid in cash or gold?

The money your uncle gave your mother to buy gold, and she died before purchasing it, is to be added to the estate and distributed among the heirs according to their legal shares. The husband is obligated to return the money to the estate, and if his daughter pays it on his behalf, he is absolved. Buying gold and distributing it among the heirs without their permission is meaningless.