Is it permissible to give Zakat money to a person to help him with his private project as a benevolent loan, and then redistribute the amount when it is repaid? And is it permissible to give Zakat money to a female relative for the completion of her marriage?

It is permissible to give zakat to the poor person who does not own enough for himself and his dependents. He may dispose of it as he wishes in a way that helps him support his family. Zakat is given to its rightful recipient as his property, not as a loan or a gift, and it must be paid to its beneficiaries without delay or installment. If your female relative is poor, it is permissible to give her zakat for her to dispose of as she wishes. However, if she gets married and becomes financially independent, she should not be given zakat, as her maintenance becomes obligatory upon her husband.