Is it permissible for a woman to travel alone to perform her religious rituals, seek knowledge, and engage in da'wah (calling to Islam), especially if no mahram is available to accompany her? And is it permissible to befriend non-Muslims or people from countries hostile to Muslims?

A woman is permitted to emigrate without a mahram (unmarriageable kin) from a country where she cannot practice her religion and is forced to abandon it upon leaving, to a country where she can preserve her religion, morals, and honor, provided it is difficult to find a mahram. However, if it is possible to find a mahram or marry a righteous man, she should ensure that the mahram travels with her to escort her and then returns.

As for befriending others: It is forbidden for a woman to have male friends. It is permissible to deal with disbelievers and sit with them out of necessity, without showing them loyalty or affection.