Is it permissible to greet non-Muslims with "As-salamu alaykum" and bid them farewell with "Fi Aman Allah," and is it permissible to supplicate for their guidance to Islam?

The majority of scholars are of the opinion that it is forbidden to initiate the greeting of peace (Salam) with a disbeliever, based on the hadith (definition): "Do not initiate the greeting of peace with the Jews or the Christians." As for saying "Fi Aman Allah" (In the safety of Allah) to a disbeliever, there is no specific text prohibiting it, and the apparent ruling is that it is permissible. This is because what is forbidden in supplicating for non-belligerent disbelievers is seeking mercy for them or seeking forgiveness for them. However, supplicating for their guidance is permissible, based on the hadith of Abu Musa, who reported that the Prophet (peace be upon him) used to say to the Jews when they sneezed: "May Allah guide you and set your affairs aright."