What is the ruling on residing with male siblings in another country for work, while there are sons of the maternal aunt present and I am performing household chores? And is it permissible to reside with a trustworthy Christian woman who respects the religion?

It is permissible for a woman to live with her brothers under certain conditions, including: having a separate place for herself where her maternal cousins cannot be alone with her, observing the legal hijab (definition) when appearing before them, and covering the awrah that must not be exposed to her brothers (the entire body except for the extremities). If the brothers are in another country at a traveling distance, she is not permitted to travel to them except with a mahram (definition). It is also permissible for her to reside with a trustworthy Christian woman, provided she maintains her awrah covered in front of her.