If God is unchanging, why does the world change if it reveals God? The answer is found in understanding the difference between the nature of God and the nature of the world. God's nature does not change. He is always the same, always consistent, always true, etc. The world, on the other hand, is separate from God. It is His creation, and it does not share in His nature. Since it is different and separate from God, it is not logically necessary that the world be unchanging.
Nevertheless, the Bible states that God is known in creation to some degree: Romans 1:19-20 says, "because that which is known about God is evident within them; for God made it evident to them. 20For since the creation of the world his invisible attributes, his eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse." When the Bible says that God's attributes can be known, it is dealing with the quality and characteristics of God. No created thing can properly represent God. All that is created bears, to some degree, His fingerprints, but each created thing does not sufficiently represent the creator. Therefore, the creation, the world, does not completely represent the nature of God, which is unchangeable.
The attributes of God can--to a degree--be seen in creation. For example, we can see from space (height, width, and depth), time (past, present, and future), and matter (solid, liquid, gas), that God is triune since each of the three properties of the universe are comprised of three parts. We might deduce that God has an aspect to His nature that is three in one since we see it reflected in nature.
We can also see that God is a God of order since the world has order. We can see that God is wise since that order provides sustenance for the created order. We can see the incredible knowledge of God in the creation of the variety and complexity of the different animals. We can see that the world did not come into existence by itself, and we can look at the beauty of a sunset and realize that God quality of beauty. It is these kinds of things that help us to see the attributes of God in creation.
But what about killing, suffering, earthquakes, famine, etc.? These are in the world, too. If the world demonstrates attributes of God, then is it not fair to say that God likes suffering since it is in the world or that God has a dark and malevolent side? No, because God did not create the world this way. He created it good. There was no suffering in the world when God created it, but with the fall, the entrance of sin into the world, suffering was also introduced, and the creation moans to be delivered from its present bondage.
Romans 8:20-22, "For the creation was subjected to futility, not of its own will, but because of Him who subjected it, in hope 21that the creation itself also will be set free from its slavery to corruption into the freedom of the glory of the children of God. 22For we know that the whole creation groans and suffers the pains of childbirth together until now."