Is the father sinful for opening an interest-based bank account for another person in which he placed a bank deposit, and what is the ruling on the heirs paying interest-based (usurious) earnings from the inheritance, and can this sin be expiated by donating an amount equal to the interest-based (usurious) earnings from the inheritance?

It is permissible to open an account in usurious banks out of necessity and due to the unavailability of an alternative, provided that no usurious interest is taken, in order to avert the greater of two harms.

There is no sin upon your father for opening an account for that person if he was in need, and your father was unaware of him taking usurious interest.

You are not required to disburse the amount of interest on behalf of your father, because he did not take anything for himself, and his sin – if any – is the sin of aiding in a forbidden act.

You should frequently seek forgiveness for your father, as this is a form of showing righteousness towards him after his death.