I can name a few off the top of my head that are right there in Genesis.
God created the world, then he created plants, then animals, then men and women, blessing them. Then the LORD, after making the earth, puts plants in a garden in Eden, puts a man in it alone, then makes animals(yes, he makes animals right there out of the ground, not earlier: "Out of the ground the LORD God formed every beast of the field and every bird of the sky..." [Gen 2:19]) in it, then creates a woman out of one of the man's rib.
I thought it was explained: Chapter 1 in Genesis is more of a Synopsis of all of Creation. It doesn't explain HOW anything was created, except that God said the words, and there it was.
God made the plants on Day 3. I don't see the problem. Just the focus of the narrative is on the Garden of Eden.
God created animals on day 5 or 6, depending on what they were. God didn't just "make them" in Chapter 2. In Chapter 2, we are treated to a few more details of HOW God created them. There is no contradiction here.
And Eve was created out of Adam's rib. In Chapter 1, it says that man and woman were created. Chapter 2 gives a little more detail into HOW God did that, and with a little more sequencing. Again, no contradiction.
And don't forget, who was Cain's wife, where did she come from
That is a good question. Jewish tradition says that both Cain and Abel (and, I suppose, Seth) were born with twin sisters. Cain married Abel's twin sister, and Abel married Cain's twin sister. The laws against incest didn't exist yet, when the only humans available to marry are only siblings.
and why is the Torah so silent about it?
Couldn't tell you. Maybe it wasn't considered a significant detail by God.
Was she his unmentioned sister? Did God just create her out of nothing for Cain despite what he did to his brother?
I asnwered that already.
And now that I think about it, before Cain even does marry his suddenly appeared wife; after God curses Cain for murdering Abel, Cain complains about being cursed by other people... who don't exist yet!
True. But they WOULD exist eventually, and when they heard about it, he feared he would be punished, cursed, and things of that nature.
At this point, the only human beings on the earth are Adam, Eve, and Cain himself.
And his wife, and Abel and HIS wife.
Cain shouldn't even fathom other nations of men yet, as he and his parents are now the only ones on earth!
Not really. The idea of more people eventually existing isn't beyond complete thought. They were born, and other people would be born. And other people, in generations beyond his parents and his wife, would learn of his crime against humanity.
I know there could be parts that are left out, but why were they left out if doing so just causes more questions and even makes some people leave the faith? A single passage about them would have sufficed.
Not everyone asks questions that make them leave the faith, especially for not understanding geneologies. It is known that God didn't include every last detail of creation, or human history in the Torah. Just because one person finds that such a thing is desperately important doesn't mean it will shatter the faith of someone else if they don't know the specific answers to those questions.
And now that I think about it, in Jewish beliefs, why did the serpent want to tempt Eve in the first place? Was he just looking for a laugh or something?
Actually, the most comprehensive answer I've ever received is in a lecture series written by Rabbi David Fohrman. I'll link to it later.
But the quick answer I've come to after studying his series is that the snake had a couple of motives. First of all, he was jealous of Adam. He wanted Eve for himself, and if Eve made Adam eat the fruit, he thought he could get her that way. (The idea makes me shudder, but it could have been possible.)
Also, the simple idea is that the snake simply introduced Eve to the concept of animal logic. Animals don't have "commandments" by God. They have instincts. God commanded Adam (and by extension, Eve) not to eat the fruit of the Tree of Knowledge of Good and Evil, verbally. But the fruit was still desirable.
The snake said that the instinct that said that the fruit was desirable was ALSO from God. And animals were expected to follow that inner voice. But humans were not LIKE the other animals, and were expected to follow the VERBAL command.
This:
Serpents of Desire: Good and Evil in the Garden of Eden. An Introduction
Is the first installation of the twelve part series. It has the introduction, ten chapters, and the conclusion.