How can God's all-encompassing mercy be reconciled with His punishment and justice on the Day of Resurrection, especially if God forgives a person who was excessive in sin and admits him into Paradise, while another believer struggled against himself and committed to acts of obedience, and then God made them equal in reward?

There is no contradiction between Allah's justice and His mercy towards the wrongdoer, and the forgiveness of their sins. Forgiveness is a bounty from Him, glory be to Him, and bounty is not justice. If He were to deal with them according to their deeds, none of them would enter Paradise. Allah forgives whom He wills and punishes whom He wills. He is the Sovereign, the Disposer of affairs, who does what He wills and decrees what He desires, and He is not questioned about what He does. Furthermore, His forgiveness of a wrongdoer does not imply their equality in status with others who are better than them.