Why does God allow Sin in the World?
Sin is not God's doing, it is ours. God can't sin. The world is in pain and we are the cause of that pain. We are the source of all the wars, diseases, anguish, and suffering on Earth! Each time we sin and refuse God, a part of our world suffers.
Why did God give us the Right to Choose?
Choice is God given. God gave humans and the Angels the right to choose. The Choice is follow God or follow our own desires (sin).
What if God created us to always follow Him, to always do what He wants us to do? To never sin, always be faithful, not having to seek perfection, 'cause we would be perfect and exactly like a robot.
Go hug a computer and see if it can return that hug. Does a computer have a choice? Can it create love? NO. Only mimick love. Only do what it was programmed to do.
God gave us a choice to love Him or hide from Him of our own free will. God created us for His pleasure.