Can non-believers be afflicted by sorcery, the evil eye, and jinn possession? If so, why would those among them who have not received the Islamic call be afflicted by such things?

Muslims and disbelievers are equally afflicted by what you mentioned. However, Allah has distinguished the believers by fortifying them with faith and righteous deeds such as dhikr (remembrance of God), prayer, and fasting. If a person becomes heedless of deeds of faith, they will be afflicted by this. The reason for jinn possession of humans may be the jinn's love for the possessed, or the human's harming of them, or merely toying with them. It could also be due to desire and infatuation, or hatred and retribution, or mischief. Furthermore, the affliction may be a punishment from Allah due to sins and transgressions, or a trial to expiate evil deeds or to elevate one's ranks.