Is it permissible to study at a co-educational university while uncovering the face out of necessity, and to work in a mixed environment with regulations, taking into account the family and social circumstances that prevent marriage and abandoning studies?

It is not permissible to study at a university where there is unlawful mixing unless there is a necessity or an urgent need. Nevertheless, the limits and etiquette of Islamic law must be observed when dealing with non-mahram men. As for uncovering the face, if you believe it is obligatory to cover it, then it is not permissible to uncover it except for a necessity or a valid need. But if you believe it is permissible to uncover it, then there is no harm, provided there is no fear of temptation (fitna).