Is an agreement to compete academically, with the winner making a request of the loser, considered a form of compensation (iwad) or gambling (qimār)? And what is the ruling if the request cannot be fulfilled or delivered? Is it obligatory to try an unreliable method to deliver the request? How can one seek knowledge for the sake of Allah in competitions of ethics, and is it permissible for the sole intention to be to win the prize?

Your agreement with your friend to obligate the winner to fulfill the other's request is a forbidden gamble, and therefore, nothing is binding upon you. As for participating in Islamweb's ethics competition with the aim of obtaining a reward, it is permissible, and it is in fact a جعالة (a promised reward for a specific act). Nevertheless, the intention should be rectified so that participation is for the sake of spreading virtuous morals and inviting others to them.