Is it permissible to give Zakat al-Mal (obligatory charity) to an unmarried sister for a dental procedure, knowing that she is unemployed and that my parents are retired and their salaries, along with my brother's, are insufficient for expenses, or is it permissible to pay it as installments on behalf of my brother who is studying at university?

Zakat has specific categories of recipients, and it is not permissible to give it to others. Your sister is eligible for Zakat if she is in need of the operation, and it is not for luxury or enhancement, and her father is unable to cover its expenses. As for your brother, it is not permissible to give him Zakat for the mentioned purpose, except in the case we explained in Fatwa no. 120245.