Hello darwinidiva, I hope you're still checking out this site. I don't know how my answers will compare to the others, I may be able to add some information to theirs.
It comes down to the intent of the author. I can't add more than that.
Jesus may not have mentioned them, but that doesn't mean they're unimportant. Jesus started the New Covenant (New Law, as you call it), but God didn't talk solely through Jesus. God also spoke through the apostles, including Paul. Let's look at the topics themselves.
I would suggest that part of the reason was to show just how hideous and deadly sin is. Sin separates us from God. Sin and perfect holiness cannot exist in the same place. Blood symbolizes the life of an organism, and by requiring blood sacrifice God showed that through sin, we lose our life spiritually, that is to say, we die spiritually. Jesus's death, which covered all of man's sin, is particularly grotesque. The beatings and wounds he received before being put on the cross shows just how disgusting and shameful sin really is.
As I said earlier, God (who is perfectly holy) cannot and will not be in the same place as sin. In addition, there's no guarantee that just because someone sees God they will come to faith. There are those who are so skeptical that they'll try to explain it away. In addition, we need to remember that God doesn't just want us to say "I believe God exists," he wants us to love him. Sure he could visually reveal himself to us, but that doesn't guarantee people will love him. If anything, it will scare them and they'll become Christians out of fear, not love. That's why Jesus didn't point his finger at the sun and throw it around the sky to prove himself to be God incarnate.
And while he may not have revealed himself tangibly, he has in other ways. I'd encourage you to look up Christian apologetics. Apologetics is the defense of the faith using reason. In my readings I've found there are many ways we can see it's reasonable to believe in God.
Apologetics315 is a good website. Look up terms like cosmological argument, teleological argument, and moral arguments. There's also the resurrection of Jesus, which has yet to be proven false, and indeed the New Testament is one of the best preserved ancient documents there are.
I probably didn't answer that very clearly. Feel free to give follow-up questions.
Yes, unfortunately they are wrong.
I think there's a bit of error in your reasoning here. Not every Christian (or Muslim, or Buddhist, or Shinto, etc.) has been taught from birth what to believe. I was raised in a household with no religion, and was myself an atheist until I was 16. Are there Christians in my family? Yes, but in more recent generations of my family it's less prominent. Although there's a Christian influence in my family, it's not necessarily a family belief anymore.
Now, is Christianity a personal truth, but nothing more? I'd disagree. The Bible - and most significantly, the life, death, and resurrection of Jesus, the core of Christian faith - has very good reason to call itself the absolute truth. In terms of archaeology and history, the Bible has not shown itself wrong and is in fact used by historians. We have thousands and thousands of ancient copies of the Bible, either fragments or entire parts, and it's been preserved with 95% accuracy. Most of that 5% inaccuracy? Spelling errors and other writer mishaps that are easily pointed out. The Bible is hardly hokey-pokey (I feel so old for saying that). I could go on, but when you consider the evidence, Jesus's words of "I am the truth" is surprisingly credible.
