Is Zakat due on delayed funds received from the mother's inheritance, and for how many years should it be calculated? And do the sisters from the father inherit from the rights of the stepmother who passed away before him?

The delayed financial entitlements of your mother from the Ministry of Education are considered a debt, and zakat is obligatory on them, with differences among the scholars' schools of thought: Qatadah, Ishaq, and Abu Thawr are of the opinion that zakat is not obligatory on it due to the inability to benefit from it. As for Al-Thawri, Abu Ubayd, Al-Shafi'i, and Ahmad (regarding a debt owed by an insolvent person), they hold the view that zakat must be paid for all past years after its collection. Whereas Al-Awza'i, Al-Layth, and Malik are of the opinion that zakat is obligatory for only one year upon its collection.

As for the father's share from his wife's (your mother's) inheritance, it is one-fourth due to the existence of children for her, as Allah Almighty says: "And for you is half of what your wives leave if they have no child. But if they have a child, for you is one fourth of what they leave, after any bequest they [may have] made or debt." This one-fourth is inherited by his descendants, including your paternal half-sisters. It is advisable to refer to the Sharia courts to resolve the matter.