Does a lack of success in an exam after supplicating for a good grade, the passing of years in a bad state, while the other party improves after their separation, indicate a sign of God's wrath and that the person is bad and undeserving of love?

What happened is not a sign of Allah's wrath; rather, it is divine decree (qadar), and one must submit to it while taking necessary measures, focusing on studies and exams, forgetting the past, and not preoccupying oneself with that person's matter. As long as repentance has been made for sins, they will not harm. One must strive in obedience to Allah, increase good deeds, trust that sustenance is apportioned, and adhere to supplication.