You have asked great questions. And though I would love to answer in as much detail as possible, for the sake of this post I will refrain from doing so. Rather, I will give a quick overview. Your concerns about certain elements in the Bible and aspects of Christian doctrine are shared by many people. I will try my best to answer.
SEXISM IN THE BIBLE
When reading the Bible, or a Bible verse, it is extremely important to read in context. The Bible contains passages that, when taken out of their respective context, may appear sexist by modern standards. However, the Bible actually displays the opposite - a profound respect for women. In the New Testament, Jesus' interactions with women were revolutionary for His time. He spoke with women publicly, had female disciples, and appeared first to women after His resurrection (John 20:14-18). Early Church leaders like St. Paul also emphasized the equality of all believers in Christ (Galatians 3:28).
SLAVERY IN THE BIBLE
Slavery in the ancient world was vastly different from the race-based chattel slavery of the modern era. For example, all workers under the Roman Empire were considered slaves of the state. The Bible contains regulations for slavery, but these were often meant to mitigate the harshness of the practice and protect slaves from mistreatment (e.g., Exodus 21:20-21). The seeds for the abolition of slavery can be found in the Christian doctrine of the inherent dignity and equality of every human being made in the image of God (Genesis 1:27).
UNBELIEVABLE STORIES
The Church teaches that the Bible contains different genres of literature, including historical narrative, poetry, allegory, and myth. The story of Noah's Ark, for instance, can be read as a theological and moral lesson about human sinfulness, divine judgment, and mercy, rather than a literal historical account.
ORIGIN OF THE UNIVERSE
The universe, "popping into existence," closely mirrors the Big Bang theory (which might have been obvious). The Big Bag theory was first proposed by Georges Lemaître, a Catholic priest and physicist. This scientific understanding of the universe having a beginning aligns with the theological concept of creation ex nihilo (creation out of nothing). The Church has long held that faith and reason are compatible. In fact, they were the primary driving source for scientific breakthroughs. They often funded many scientific thinkers and their projects.
ETERNAL SUFFERING
This is the main issue I wanted to clarify. God desires all people to be saved (1 Timothy 2:4) and extends His grace to everyone. However, human beings have free will to accept or reject God's love. The Church teaches that God judges people based on the knowledge and grace they have received. The concept of invincible ignorance acknowledges that those who, through no fault of their own, do not know Christ but seek the truth and do God's will as they understand it, can be saved (Lumen Gentium 16).
A common misunderstanding is that God sends people to hell. However, it is us who send ourselves to hell through our choices. A byproduct of our free will is the ability to make decisions, which can go against God's divine laws. When this occurs, we sin. For instance, God commands us not to lie (Exodus 20:16, Leviticus 19:11). If we deliberately lie, we have committed a sin. Everyone falls short of the Kingdom of Heaven in one way or another because because of our sinful nature (Romans 3:23).
The condition to enter heaven is perfection, a state of being sinless. However, Jesus Christ, in His perfect nature, came down from Heaven to undergo the penalty of sin (hell) for our sake. Through His sacrifice, we are offered redemption and the possibility of eternal life with God in Heaven.
To answer your question, the notion that someone born into a Muslim household is "sent" to hell is not accurate. The Church believes in God's universal salvific will, meaning He desires everyone to be saved. Salvation is accessible to all, no matter what household they are born in. Ultimately, God's judgment is just and merciful, taking into account each person’s circumstances and intentions. Thus, the idea of automatic damnation for someone based on their background does not align with the Church’s understanding of divine justice and mercy. Let me know if I understood your question correctly.
CONTRADICTIONS
If you can give me any contradictions I will happily take them up.
How much of the bible do I think is the actual Word of God, and how much of it do I think is flawed by the workings of man?
I believe the Bible, in its entirety, is the Word of God.