Does Zakat become obligatory on money you inherited from your father, knowing that your mother used to deal with it through a usurious bank, and are you required to pay Zakat for past years if the money no longer reaches the Sharia-stipulated minimum (nisab) currently?

What was previously spent from usurious gains does not need to be replaced. However, your mother must repent for depositing money in a usurious bank. As for the remaining usurious gains, they must be disposed of in charitable causes. If the remaining money is from the original inheritance and not from usurious gains, then it is lawful, and Zakat is due on it if it reaches the nisab and a full year has passed. The Zakat for past years is not waived, as it does not lapse with time, and there is no sin upon you for its delay.