Is it permissible to have affection and familiarity with a devout Christian American family with whom a Saudi student is residing, while maintaining prayers and religious rituals, benefiting from learning English, and teaching them something about Islam?

A Muslim is not permitted to show affection towards the enemies of Allah Almighty under any circumstances, as this poses a danger to his religion. The mentioned benefits of learning the English language or inviting people to Islam can be achieved without cohabiting with them.