Is it permissible for a father who works in a bank to help his daughter with her wedding expenses, knowing that she has no income?

If your father works in a usurious bank, then his salary is ill-gotten (haram) wealth. Some jurists permit accepting gifts from ill-gotten wealth if it is not related to the right of an individual, such as stolen or usurped property. Therefore, there is no blame upon you for benefiting from what he gifts you for marriage or other purposes.