What is the optimal way to act when in doubt about statements and actions from those around us that bear the suspicion of mocking religion, or that may amount to disbelief, especially when it is impossible to leave the place, and is it obligatory to warn everyone who commits what is suspected to be an act of disbelief?

The questioner must turn away from the whispers of takfir (declaring someone an apostate) and stop thinking based on doubt and assumptions. The ruling of kufr (disbelief) is not a light matter, nor is it a domain for the general public. As Al-Qari said: "If a statement made by an ordinary person can be interpreted in ninety-nine ways as kufr, and one way as not kufr, it is not permissible to rule him an apostate." A specific individual who commits an act of kufr is not ruled to be an apostate unless the conditions for takfir are met and its impediments are absent. The questioner should denounce evil to the best of her ability, as it is haram (forbidden), without ruling someone a disbeliever or even thinking about it. The whispering of takfir against others is harmful and destructive.