Is it permissible to give Zakat to relatives if the maternal aunt is in a moderate financial situation? And is what the father paid to his sister-in-law (maternal aunt), who requested money to pay off a debt and marry off her daughter, considered Zakat, especially since the mother did not inform the maternal aunt that the money was Zakat?

If your paternal aunt is indebted or poor, unable to meet her needs, your father may give her from the Zakat. If her daughter needs to marry and requires provisions for it, the Zakat should be given directly to the daughter, with the caveat that there should be no extravagance in the marriage. If her role is to serve her husband, and this is in exchange for Zakat, it is not permissible. It is permissible to take Zakat for marriage expenses if one cannot earn enough to cover them, because marriage is part of completing one's sufficiency. Giving charity to deserving relatives is better, as it combines charity and maintaining kinship ties. It is not a condition to inform the recipient that it is Zakat if they would be offended by such knowledge.