Is it permissible to give my Zakat on money to my mother so she can spend it on my siblings for their study expenses, clothing, and food, knowing that I am the eldest sister and unmarried, and they are likewise, and we live with our mother, and our father is not present, and our mother is the one who provides for us?

You are not obliged to financially support your poor siblings according to the majority of scholars, and it is permissible to give them Zakat. If your siblings are adults, you should give them Zakat for them to spend on themselves. It is also permissible to give it to your mother as their agent if she is unable to support them. However, if she is able to support them, then they are considered wealthy due to her obligatory support, and thus Zakat should not be given to them or to her. It is not permissible to spend Zakat on education expenses except for the poor who are unable to afford study costs and those they support, and under certain conditions, including: their eligibility for knowledge, their inability to combine education and earning, and that the knowledge is something Muslims need, such as Islamic sciences, engineering, and medicine.