Why did Allah forgive Adam after his disobedience and expel him from Paradise, but not forgive Iblis after his disobedience and destine him for Hellfire? And how could Iblis disobey his Lord when he is predestined, not given free will?

A Muslim must believe that Allah Almighty does what He wills and judges with justice, and He is not questioned about what He does. There is no comparison between Adam and Iblis. Adam, peace be upon him, repented and sought forgiveness, whereas Iblis refused, became arrogant, rebelled against the Creator, and persisted in his transgression. Iblis and others among jinn and humans have free will in their actions; they have volition, capacity, and choice in obedience and disobedience, but their will is only executed by Allah's command.