First, doubt is a necessary part of faith because faith does not mean 100% certainty. Faith means believing what God has said is true despite what you may see around you. Sometimes you believe because of what you see; sometimes you believe in spite of what you see.
Many people think doubt is the opposite of faith. That’s not true. Unbelief is the opposite of faith. Unbelief is the settled conviction that what God says is not true. Doubt speaks to the inner uncertainty that we all have from time to time. As long as we live in an imperfect world, we will all deal with doubt from time to time. Some will struggle more, some less, but everyone has their doubts from time to time.
See If I Believe, Why Do I Doubt?
Second, there is no single answer to the question of why God permitted evil. Or perhaps we can give one answer and admit that we don’t fully understand it. Part of the answer must be that God allows evil in the world in order to display the riches of his grace in Christ Jesus. Without sin, there is no need for mercy and no need for grace. But where sin abounded, grace super-abounded (Romans 5:21). God allows evil, including natural disasters that are the result of evil, but he is not the direct cause of evil in the universe. But now that evil has been let loose, we see God’s grace magnified in the offering of his Son, the Lord Jesus Christ, who “became sin for us” (2 Corinthians 5:21) that we might be made the righteousness of God in him.
See Why Is There So Much Suffering In The World?