Is it permissible for me to give my Zakat to my minor siblings and my mother, especially since I am unemployed and saving my money for studies, and our retirement income is insufficient for our needs, and my siblings have private funds that cannot be disposed of? And is it permissible to consider the repair of my mother’s car as Zakat?

It is permissible to give zakat to siblings if they are among the eligible recipients of zakat and are in need of it. If the money saved for orphans at an orphan institution is available to them and sufficient for their basic needs, then they are considered wealthy and are not eligible for zakat, because orphanhood alone is not a reason for zakat eligibility. As for the mother, it is not permissible to give her zakat due to your obligation to support her, except in exceptional cases. If it is permissible to pay zakat to her, then repairing her car with it is not sufficient unless she authorizes it. The money saved for study or the money saved for orphans at the institution is subject to zakat if it reaches the nisab and a full year has passed on it.