Is zakat due on money lent to a brother? And should the lender or the borrower pay it? And when should it be paid if no date has been set for the repayment of the debt?

The wealth you have with your brother is subject to zakat along with your own wealth if your brother is solvent and not procrastinating. However, if he is in straitened circumstances or procrastinating, then there is no zakat on it until you receive it. Once you receive it, you pay zakat on it for one year.