What is the authenticity of the story of the unbeliever who used to throw trash at the Prophet’s house, and then the Prophet visited him when he fell ill because he had stopped throwing trash? And is it true that the Prophet ﷺ never visited an unbeliever except to invite him to Islam?

The story mentioned has no basis in the books of Sunnah. However, another authentic Hadith states that a Jewish boy used to serve the Prophet, peace and blessings be upon him. The Prophet, peace and blessings be upon him, invited him to Islam, and he embraced it. The Prophet, peace and blessings be upon him, then departed, saying: "(All praise is due to Allah, who saved him from the Fire)." It is permissible to show kindness and gentleness to a non-combative disbeliever and to give charity to him, without showing him allegiance or love in the heart. This should be done with the intention of inviting him to Islam, while adhering to the guidelines for dealing with non-Muslims, such as not showing them allegiance and treating them well as long as they are peaceful. It is also permissible to engage in trade and other dealings with them. Teaching the two Shahadas to a sick disbeliever is a good deed, as it is an invitation for him to embrace Islam.