Is there a reward for those who recite the Qur’an in a group and in competition, and is there a reward for those who compete in memorizing the Qur’an, given the presence of the intention of showing off in both cases?

Agreement upon reading, memorizing, and cooperating in [the study of] the Qur'an is a good matter, falling under the category of cooperating in righteousness and piety, and competing in good deeds; as Allah Almighty says: "And for that let the competitors compete." (Qur'an 83:26). The condition for this is sincere intention for Allah Almighty, seeking His countenance and hoping for His reward, while being careful not to let Satan deter one from doing good out of fear of falling into ostentation. For the wise person does not abandon good deeds out of fear of ostentation; rather, he acts and is sincere therein for Allah Almighty.