What is the ruling on befriending and hosting Christian families in a non-Muslim country, and accepting gifts from them? And is it permissible to host and befriend a non-observant Muslim family that does not pray, while it is permissible to continue working if one of them is the manager?

It is not permissible to exchange visits with a female director who does not pray if there is a fear of harm and corruption resulting from it. Knowing that she is a woman does not prevent working with her, unless there are Sharia-prohibited aspects such as unlawful mixing. It is permissible to accept a gift from a non-Muslim under specific conditions.