Is it permissible to take a portion of my brother's Zakat to repay his debt, knowing that my salary is only sufficient for necessities, and without informing him of this?

You may take from Zakat if you are in debt and unable to pay off your debts. As for taking from your brother's Zakat without his knowledge, there is a difference of opinion among scholars regarding whether it is permissible for an agent to take from what he has been entrusted to distribute to the poor, if he himself is eligible.