Is it permissible for a woman to work as an investigator or a ship captain, given the implications of khalwa (private seclusion) with men and travel without a mahram (unmarriageable kin), and is it permissible for her to travel alone for work or study if she is capable of protecting herself and committed to religious observance, and is it permissible for her to travel with her mamluk (male slave) considering him a mahram?

It is permissible for a woman to work if her work is free from Sharia prohibitions, such as mixing (free intermingling) and khalwa (private seclusion) with men. It is not permissible for a woman to work as an investigator or a ship captain unless her work is free from these prohibitions. A woman traveling without a mahram for work or study is Islamically forbidden. The reason for the prohibition is the woman's travel without a mahram, not the purpose of the travel or the woman's condition. It is not permissible for a woman to travel with her slave, because he is not a mahram.