Do female employees bear responsibility for squandering public funds and committing forbidden acts when forced to carry out personal tasks for officials and their children using work resources and official working hours?

The work tools under an employee's hand are a trust (amanah) that must be preserved and not neglected. It is not permissible to obey supervisors in neglecting them, because there is no obedience to a creature in disobedience to the Creator. Fear of them is not a justification for carrying out their orders that violate the Sharia, and one can complain to those higher up than them.