Is it permissible for a student to do charitable deeds with the intention of succeeding in exams? And is it permissible for him to place dates, water, and sweets in the mosque and ask the worshippers to pray for him?

It is permissible to intend by good deeds closeness to Allah, along with the intention of success in exams. What is prohibited is performing an act of worship solely for a worldly purpose. It is permissible to ask people for supplication, but it is better for the giver of charity not to ask the recipient for supplication, as this might deviate from feeding for the sake of Allah.