Is it permissible to donate the interest from money deposited in a usurious bank without the owner's knowledge, especially if I am asked to retrieve the money from the bank? And is it permissible to pay the value of the interest from my own money, or to replace it with my money after withdrawing it from his? And how can past interest be estimated if the deposit date is unknown?

The profits from interest-based banks are forbidden (haram). The son should gently and wisely advise his father to stop dealing with them. If the father believes it is permissible based on a fatwa from a scholar, he may be excused by Allah, provided he is not following his desires. For whoever asks the people of knowledge and acts upon their fatwa, there is no sin upon him. Although the fatwa permitting investment interest (riba) is incorrect, it is permissible to eat from the money of someone who deals in interest without sin, while continuing to advise him. Do not dispose of your father's money without his permission. You are not required to give charity on his behalf from your own money equal to the amount of the interest-based profits, but you may donate charity with the intention that its reward be for your father.