Is Zakat on money and its hawl (passage of a year) calculated from the day of the father's death or from the day the inheritance is received from the bank, especially for a frozen deposit with a return that has not yet reached the nisab after disbursements from it?

As soon as the deceased passes away, their inheritance is transferred to the heirs by operation of law, even if they cannot dispose of it. Thus, your father's estate became your property the moment he died. Whoever's share reaches the nisab (threshold) must pay its zakat when a full Hijri year has passed since your father's death. The inability to dispose of the money during this period does not affect the obligation if the year has passed and it becomes possible to dispose of it.

As for the deposit, if it is in an interest-based bank, then one must repent, withdraw it, and dispose of the interest earnings by spending them on Muslim welfare or giving them as charity. The principal amount is subject to zakat for whoever's share reaches the nisab. If it is in an Islamic bank, then the principal amount and any remaining profits are subject to zakat when a full Hijri year has passed, because the profit follows the principal. What is spent during the year is not subject to zakat.