Is it permissible to pursue midwifery studies and work in a hospital that meets the Sharia requirements in terms of dress code and dealing only with women, in order to gain the necessary experience to contribute to women's healthcare?

There is no objection to working as a midwife, whether paid or voluntarily. It is permissible to study and work in a hospital for the necessary period, especially since the hijab (definition) and prayer are allowed. One must wear the hijab and modest clothing when leaving the house, and then wear the uniform in the hospital. As for baring the forearms, it is not permissible in the presence of non-mahram (definition) men. One must strive to cover them with medical gloves or whatever covers them. The entire woman is 'awrah (private parts) except for the face and hands, according to some jurists, and covering the forearms is unanimously agreed upon if there are non-mahram men present.