Is it permissible to use charity money designated for distribution to the poor to pay off a university installment debt for a needy brother, knowing that the donor is well-off, and does this fall under the principle of "Your closest relatives have the first right to your kindness"?

You are entrusted with the charity, and it is not permissible for you to give it except to one who is characterized by poverty. If your brother is capable of working, earning, and continuing his studies, it is not permissible for you to give him from it, because he is rich by virtue of his ability to earn, due to the Prophet’s (peace and blessings be upon him) saying: "If you wish, I will give you, but there is no share in it for a rich person nor for a strong, earning person." However, if he cannot combine studying and earning, then his studies should be considered: if they are in something beneficial that the Ummah needs, such as Sharia sciences and medicine, then it is permissible to give him. Otherwise, no. But if he incurred a debt for a permissible purpose and had no money to repay the debt, it is permissible to give him from the zakat to settle his debt if the giver of zakat did not specify its disbursement.