Is it permissible for a woman to work as a teacher in boys' high schools, while adhering to modesty and decorum? And what are the conditions for her going out to this work if it is permissible?

It is not permissible for a woman to work as a teacher for boys in the secondary stage, because students at this stage are usually adolescents, and the nature of teaching necessitates interaction. It is not permissible for a woman to interact with men, due to the Almighty's saying: "And when you ask them for something, ask them from behind a screen."