What is sin?
Sin is any choice we make that is not consistent with the law of God.
How did sin get into God’s perfect world?
Sin came into the world when Adam and Eve ate the fruit of the tree from which God had forbidden them to eat.
Why did God allow sin to enter into His perfect world?
God has only told us that He wills all things for His own glory. This would include the entrance of sin into the world.
Where does God teach us that all things exist for His glory?
Paul teaches this in Romans 11: For of him, and through him, and unto him, are all things. To him be the glory for ever. Amen. (Romans 11:36) which could very well be paraphrased as:
Now the reason we praise God in this way is because all things originated from God’s purpose; all things came into being through God’s creating out of nothing; and all things are here to show forth the glory of God. source
Where are we taught the entrance of sin into the world?
This history is given us in Genesis 3.
What does “bruise” mean in Genesis 3:15?
Just from the word itself, it is difficult to know its meaning since it occurs so rarely in Scripture; see here. Fortunately, Paul decides the issue for us in Romans 16 where he makes a reference to Genesis 3:15:
And the God of peace shall bruise Satan under your feet shortly. The grace of our Lord Jesus Christ be with you. (Romans 16:20)