What is the zakat nisab on a deceased father's estate, and what is the period for which zakat is due, given that he left a bank deposit, rented properties, and land?

We ask Allah to have mercy on your father. Zakat (definition) is calculated based on the Hijri year. Regarding your question:

Firstly: The money deposited in the bank is subject to Zakat because it is productive wealth that has reached the Nisab (definition) (minimum threshold). Its amount is a quarter of a tenth (2.5%) for each Hijri year in which your father did not pay Zakat, because Zakat is not forfeited by the passage of time.

Secondly: Apartments and shops intended for personal use (not for trade) are not subject to Zakat, based on the Prophet's (peace be upon him) saying: "There is no Sadaqa (Zakat) on a man's slave or his horse." Zakat becomes due on the rent received from leased properties, if it reaches the Nisab and a Hawl (one lunar year) passes over it.

Thirdly: If your father bought this land with the intention of trading, it is considered a trade commodity, and Zakat is due on its value at the end of each year, amounting to a quarter of a tenth (2.5%). You are obligated to pay Zakat for the years in which your father did not pay it. However, if it came into his possession through means other than a trade contract (such as inheritance), or if he bought it without the intention of trading, then there is no Zakat on it.