Is it permissible to eat the sweets that a student brought but did not eat completely, and what should the student have done?

Accepting a gift from a woman to a non-mahram man and vice versa depends on the circumstances. If there is suspicion or fear of fitna (temptation/strife), then it should not be accepted. However, merely exchanging and accepting gifts is permissible, as Umm Sulaim gifted food to the Prophet, peace and blessings be upon him. Al-Shawkani mentioned the permissibility of accepting gifts from a non-mahram woman and the legality of gifting food.