Is it permissible to employ veiled women and have mixed-gender education (with segregation of sexes) in a computer institute whose intention is to benefit the nation and for the sake of Allah, and what is the stance if the partners refuse non-mixing in a country where they consider it permissible?

If there is no need to employ women in the institute, then it is preferable to employ men, due to the religious caveats and conditions associated with women's employment. However, if there is a need to employ them, then there is no harm in it, provided that they adhere to the Islamic hijab, avoid mixing with men, and do not wear perfume. As for the presence of male and female students in one hall with differentiation, there is no objection to it, provided that female students adhere to the hijab, do not wear perfume, and do not wear adornments; otherwise, it is not permissible to establish the institute. Those in charge of the institute should be keen to observe the Sharia of Allah and avoid gathering men and women in one place as much as possible. The questioner should strive to convince his friends to observe the Sharia guidelines; if they refuse, then he should not participate with them.