Is zakat obligatory on money collected and invested to face calamities, and is it permissible to pay zakat to this charitable fund?

There is no Zakat due on the aforementioned money, as it is considered an endowment (waqf). Whether the money is frozen or invested in trade, it is not permissible to pay Zakat on it because it is not designated for the poor or other Zakat expenditures.