Is Zakat considered paid if given to an intermediary without knowing whether he delivered it or not, despite his assurance of delivery? And is Zakat permissible for a single brother with a low income, as well as for student siblings who are unemployed in a large family supported by the father?

It is permissible to give Zakat to someone trustworthy to deliver it to those who are entitled to it, and it is considered paid unless it is proven that the agent did not pay it, in which case it must be given again. It is permissible to give Zakat to a brother with a low salary that is not sufficient for him, and to poor students who do not have enough and cannot earn it. In fact, giving it to them is better because the Zakat payer is not obligated to support them. However, if they are not poor, it is not permissible to give it to them.