Will a Muslim be held accountable for raising his children in non-Islamic countries, far from mosques and Islamic schools, and for the evils he witnesses in public? And is he obligated to inform his friend that he saw his wife alone with a strange man, given the unavailability of four witnesses, and would his failure to inform him be considered a betrayal?

The general rule is to prohibit a Muslim from residing in the lands of the disbelievers due to the danger it poses to their religion and morals, unless they are able to openly practice the rituals of their faith and are safe from temptation. If you fear temptation for yourself and your children, then it is not permissible to remain. However, if you are safe and in need, then you must protect yourself and your family with knowledge, patience, and struggle, and you must lower your gaze from forbidden things. As for your friend's wife, if you witness her committing a forbidden act, you must advise her, warn her, and inform her husband if she does not repent. If that does not help, then you must alert her husband and inform him.