Is zakat obligatory on the entire saved amount (that which is with the father, and that which is with his friend for trade), or only on the amount he possesses?

Your father must pay zakat on all his money, both what is in his possession and what he gave to his friend for trade, because the zakat on Mudarabah capital is due on its owner. The trade goods should be valued, and their value added to the existing cash to pay one-quarter of one-tenth (2.5%).