Is Zakat obligatory on the deceased father's wealth for a period of 12 years, with doubt as to whether it was paid, and can it be paid in installments, and how is it calculated with the changing value of money?

You are not obligated to pay out money, as the fundamental principle is that your father’s financial obligation is cleared and that he fulfilled his duty, and this principle should not be deviated from except with certainty. However, if you become certain that your father did not pay the zakat (definition) on his wealth, then you must pay the obligatory zakat from your share of the inheritance, and advise the remaining heirs to do the same.