Is the failure to achieve a goal, after supplicating for it, a punishment for shortcomings? And is it possible to supplicate for a change in the outcome now? And is striving diligently in study, despite depression, a condition for the supplication to be answered?

As long as there is a chance for success, you must exert effort in studying and achieving, while supplicating and relying on Allah, without dwelling on what has passed. Rid yourself of sorrow and despair through diligence and having a good opinion of Allah, for Allah is capable of granting you success if you take the necessary means. Your supplication is not an transgression as long as success is possible. Let what happened be a lesson to avoid future shortcomings.