Is it permissible for a brother to pay the Zakat on his wealth, derived from managing his deceased father's business at a rate of 30%, to his needy and unemployed siblings?

The aforementioned wealth transferred to the heirs upon the father's death, and the will to manage the business is void. The wealth must be divided among the heirs. If each heir knows their share, there is no objection to the heirs agreeing that one of them manage the business.

As for Zakat (definition) on the wealth, if it became due after death, then each heir owes Zakat on their share if it reaches the nisab (definition) and a hawl (full lunar year) passes while it is in their possession. It is permissible to give Zakat to poor siblings who do not possess enough to suffice them. If Zakat became due before the owner's death, it must be paid before dividing the wealth, and it is permissible to give it to his poor children.

One cannot rely solely on fatwas concerning inheritance matters; rather, they must be brought before Sharia (definition) courts for investigation and distribution of the inheritance among the heirs.