How can one reconcile the prohibition against befriending disbelievers with the desire to invite them to Islam and build bridges of trust with them? What is the difference between the 'mawaddah' (affection/friendship) mentioned in the verses and the desire for mercy towards them? Is it permissible to initiate greeting non-Muslims with "Salam," given the existence of verses that may be understood to the contrary?

One must differentiate between the actions of the heart and the actions of the limbs when dealing with a disbeliever. Love and affection in the heart for a disbeliever are forbidden. However, good treatment, righteousness, justice, benevolence, and good manners are permissible actions of the limbs towards them, as long as they do not lead to corruption.

Loving a disbeliever for their religion or for a religious trait in them is forbidden. As for natural love resulting from innate disposition (such as a parent's love for their child) or from good treatment, it is not forbidden. However, it must be accompanied by detesting their religion and disavowing their disbelief, while still wishing good for them and being keen on their guidance.

Scholars differed on the ruling of initiating a disbeliever with greetings (Salam). Some permitted it, citing Quranic verses. Some restricted it to necessity and benefit. Others prohibited it, citing prophetic traditions, including: "Do not initiate the Jews or the Christians with Salam."

As for returning the greeting of a disbeliever if the Muslim is certain that they uttered "Salam," the more preponderant view is the permissibility of returning it by saying: "Wa 'alaikum As-Salam" (And upon you be peace), because it falls under justice and benevolence.