Is it permissible for a Muslim residing in a non-Muslim country to initiate a greeting to a non-Muslim with something other than "Al-Salam," such as "Good morning," in workplaces or to neighbors, and does the ruling on this type of greeting differ from the ruling on initiating "Al-Salam" to them?

It is permissible to initiate a greeting with disbelievers other than the Islamic greeting (Salam). It is not permissible to initiate the greeting of Salam with a disbeliever, but if they greet you with Salam, you must respond by saying "Wa Alaikum." There is no objection to inquiring about their well-being and that of their children, especially if there is an Islamic benefit in doing so, such as encouraging them to embrace Islam. It is permissible to initiate a greeting with disbelievers for a preponderant benefit or to ward off their harm.