Is it permissible for a female teacher to work in a girls' high school managed by a man, where covering the face is not allowed, given that there are no schools free of men in the country, and if it is not permissible, what is the ruling on the earned salary, and is it permissible to perform Hajj with it?

If you are in need of work and no other is available, then there is no harm in continuing in it, provided you adhere to the Shariah guidelines, such as not being in seclusion [with a non-mahram], not speaking softly and enticingly, avoiding adornment and perfume, and covering the face if possible. However, if you are not in need of it, then you must leave it to safeguard your religion.