What is the Shariah ruling regarding delayed Zakat for the deceased, and is it considered a debt owed by the heirs, and what are the consequences of not paying it, and to what extent is it permissible to waive part of the inheritance for the needy and consider it Zakat?

Zakat (definition) must be disbursed from the inheritance immediately and in a single payment, because it is a right of the poor and not a right of the heirs. The heirs receive what remains after the will and debt. It is not permissible to consider the questioner's waiver to his sister and her mother as part of Zakat.