Why Are Animals Different from Humans, According to the Bible?

I think the best answer is to tell the story of God's desire to create people that he can be in relationship with. He made the world with a desire to have a special relationship with people that He would make in His own
image. The idea isn't that He doesn't care about animals or anything else that He has made. Rather, the idea is that in His infinite creativity, God wanted to share as much of Himself as He could with us. 

So human beings were the pinnacle of His creation, the highest form of life that He created. This is what it means that we were made in His image. He made us to have the capacity to know Him and to relate to Him. One picture that the Bible gives of the relationship between God and human beings is that of a father to his
children. God wanted to create a world where people could relate to Him as family, and He created the rest of the world to be the environment where that relationship could exist and flourish. So the world God created teaches us all about Him and what He's like. The world also shows us how we can live lives that would imitate Him. I believe this is why He created so many forms of life that aren't in His image. These other forms of life are gifts from God for us to enjoy and take care of and to use. These become an opportunity for us to reflect God's care and stewardship--celebrating what is good and using what is useful. All that we do in relationship to the rest of creation is to bring about abundant, teeming, fruitful, and flourishing life. God gave us a world that was very good, and our stewardship of the world was designed to make it even better.

So in relationship to other forms of life that we are stronger and smarter than, we get a very sincere opportunity to taste a little bit of what it's like to be God. All that we do should reflect God and how He treats us (with appropriate differences and qualifications).

Very practically, animals are gifts from God to us so that we could learn more about Him and be reminded of what He is like. They are gifts given to us to help us flourish. They are opportunities for us to learn how to be
good stewards and increasers of multiplying life.

Why is the world so screwed up? Is it God's fault?

This is a complicated question. There are lots of layers both in understanding what the Bible says God's perspective is on this subject, and then also how God's perspective impacts the people who are experiencing the brokenness of the world. Here's one effort to offer a simplified explanation of how to think about this:

1. God is love.
2. God made the world and filled it with people that He wanted to love to have love Him back.
3. Love requires free will. If you can't choose, or you are forced to choose, it's not love.
4. Human beings have used their free will to do evil:  to themselves, to other people, and to the world.
5. The good people and the good world have been vandalized and corrupted by the evil things people have done.
6. The evil things people have done has taken control of the world and become almost a ruling power in and of itself, being further propagated in the world. 
7. God loves and cares so much that He has consistently acted to re-engage with the world that has banished Him, to rescue people from the power of evil, and to renew them so that they can fix what has been vandalized and corrupted.
8. God loves and cares so much that He actually entered into the world in Jesus to be a human strong enough to overcome the power of evil in the world. 
9. God and cares so much that He entered into our broken world and experienced the full evil of the world and of people in His suffering on the cross. His suffering was Him taking on the consequences of the evil of people. He did this to bring forgiveness from God for the evil the we do, and to bring power into the world so that other people could receive that power and overcome it in their own lives. His resurrection shows that He is stronger than the world's evil. When we believe and follow Jesus, we receive His power. Overcoming evil in our lives means having the strength to endure the evil and brokenness of the world in our own personal lives and to be able to respond to it all with grace, understanding, love, and the strength to show others a better way.

Christmas is a chance to celebrate that we have a God who didn't destroy evil people from up in heaven, but He came into the world to rescue and renew it.