What is the ruling on working in programming graduation projects or solving exam questions for a fee, and is there any doubt concerning earning money from this work?

It is not permissible to cheat or betray trust, such as completing graduation projects or answering exam questions on behalf of students, even if the exam allows for open-book access; because cheating is forbidden by Islamic law, and the head of the department does not have the authority to permit it.

Earning from a forbidden act is not permissible, based on the saying of the Prophet, peace and blessings be upon him: "Indeed, Allah, the Almighty and Majestic, if He forbids the eating of something, He also forbids its price." Accordingly, it is not permissible to hire for forbidden benefits, nor is it permissible to take compensation for them.

What was offered to the questioner by his colleague does not permit him to purchase these projects to sell them to students, as that would be cooperation in sin and aggression.