Is it permissible to give a needy brother from the Zakat funds designated for a specific region, so that he may repay a debt he owes to the questioning brother, knowing that his income is very limited?

If your brother is poor and eligible for zakat, it is permissible to give him from the charities designated for his region without any conditions or considering it a substitute for money you have given him. There is no harm in accepting what he gives you voluntarily afterward.