I thank the Lord that you take so much interest in Him. You are on the right path to complete knowledge of the truth. And the truth shall set you free. To encourage you to continue on your quest for truth I will give you a one sentence answer for each of your inquiries.
Why won’t amputees heal?
God is able to heal any person’s sickness; you might want reconsider your label on amputees.
Why are their so many people starving in the world?
Humanity is naturally selfish and greedy.
Why does God demand the death of so many innocent people in the Bible?
The scriptures you quoted are based on Old Testament law that is no more; thanks to the death, burial and resurrection of Jesus Christ you don’t have to die in sin.
Why does the Bible contain so much non-scientific nonsense?
The Bible is filled with much scientific evidence from the finite beginning of the earth to the completed prophesized kingdoms in history as opposed to most of scientific study which is based on theories and hypothesis or in simpler terms, improbable and inconceivable chance.
Why is God such a huge proponent of slavery in the Bible?
The scriptures you quoted speak of servants or maids and home staff; again, you might want to reconsider your label on people in the service industry neither should you label the United States as unintelligent in recent history.
Why do bad things happen to good people?
Jesus himself said “No one is good, but One, that is God”.
Why didn’t any of Jesus’ miracles in the Bible leave behind any evidence?
He left you a detailed text containing 66 books with multiple witnesses to those miracles; besides living during that time you should try studying the Bible in its entirety.
How do we explain the fact that Jesus has never appeared to you?
Why would Jesus want you to eat his body and drink his blood?
It is figurative to symbolize the death, burial and resurrection that Jesus went through for your sake; instead of tasting that dreadful taste of a torturous death you have the undeserving privilege to taste bread and grape juice.
Why do Christians get divorced at the same rate as non-Christians?
Christians are human too.
Some Word from God to think about:
1 Corinthians 1:18 For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God.
1 Corinthians1:21 For since, in the wisdom of God, the world through wisdom did not know God, it pleased God through the foolishness of the message preached to save those who believe.
1 Corinthians 1:25 Because the foolishness of God is wiser than men, and the weakness of God is stronger than men.
1 Corinthians 2:13-14 These things we also speak, not in words which man’s wisdom teaches but which the Holy[aSpirit teaches, comparing spiritual things with spiritual. But the natural man does not receive the things of the Spirit of God, for they are foolishness to him; nor can he know them, because they are spiritually discerned.
1 Corinthians 3:18-20 Let no one deceive himself. If anyone among you seems to be wise in this age, let him become a fool that he may become wise. For the wisdom of this world is foolishness with God. For it is written, “He catches the wise in their own craftiness”; and again, “The LORD knows the thoughts of the wise, that they are futile.”
I hope this answers your questions. I encourage to keeping seeking and I have faith that you will find what you are looking for. God Bless you.