Is it permissible for a girl who wears the hijab and niqab to work in places where men and women intermingle, such as banks and companies, even if these places include sections designated for girls and women?

A woman's work in mixed-gender environments is subject to regulations. As for working in a bank, if it deals with transactions that are compliant with Sharia, then there is no objection, provided the regulations for mixed-gender work are observed. However, if it deals with usury, then it is not permissible to work there. It is permissible for a woman to work in places designated for women, as long as she adheres to Sharia-compliant transactions.