Disclaimer: Everything expressed in this post is my opinion, nothing more, nothing less.
Do we have free will? There is ample religious scripture and dogma to support that notion. Above and beyond all that – if we do not have free will then every act, every action, good, bad or otherwise is already pre-determined. If this is the case it logically eliminates the possibility of morality – there can be no morality if we cannot choose our own actions. Do we not, on a fundamental level, feel a sense of gratification when we do what we know to be right? Like being kind to others? Conversely, do we not feel equally bad when we do what we know to be wrong? Like doing harm to others? Logically, I must conclude we have free will.
Does humankinds acting on free will cause problems in the world? Clearly from our perspective it does. But from God's perspective? If God is omniscient and omnipotent then God must know that these problems will happen if we have free will. Therefore, God must desire us to face these problems. What great story (Novel, Play, Movie, short-story, etc.) has ever been told that lacked conflict? We have been created, and are hardwired, to face challenges and to overcome them. I don't mean to say that there will always be a "happy-ending" but that we are meant to face challenges and seek to rise above.
Does God make mistakes? If the universe does not function as intended, then yes. But unless we can sit down with God and have a friendly chat it's impossible for us to know for sure