So how come Adam is the one who caused the problem of humanity. The serpent and his satans were there all the time causing people to commit many sins more than Adam.
Also God knew from the start that Eve and Adam were going to eat from the tree, and the satan is the one who will deceive, because he created them all. OTHERWISE, the GOD who doesn't know what his creatures will do in the future is NOT a GOD, and doesn't deserve to be worshiped.
Here, you're quoting alot from Paul's letters, which many scholars have disputed their authenticity. The OT is more authentic because it was written at the time of Jesus.
I want also to say, how come everyone is a sinner. What about the baby who died before completing his first year ? what was the sin he did ?
You're raising enough questions here that it's going to be hard to give you a coherent answer. There are several references to punishment or judgement in the NT. Jesus talks about judgement all the time (think if the sheep and the goats, and many other places). The Revelation to John is all about it. Every one of these speaks of judgement, not reincarnation.
I agree that the OT is less explicit about what happens after death.
Ebia is right that the Bible, whether OT or NT, speaks in symbols. So I don't agree with people who think they know the details of what is going to happen when. However the one thing all part of the tradition agree on is that we will all be accountable to God.
I don't see any basis for someone thinking that the worst that could happen is that he will end up back on earth. The concept in the Revelation, and I think even the OT, is that at the end God will bring about a restoration of the earth. (Rev 21, Is 66:22-23; I pick Isaiah sort of at random; most of the prophets have a vision that God will eventually judge the world and restore it). If the Biblical view is right, there won't be anyplace for someone to go back to. There will be just the new creation and destruction. Whether destruction is the second death or eternal torture is less clear I think. But coming back to earth as it is now, no, I don't think there's any room in the Biblical view for that.
I think for an atheist the most dangerous position is "nothing can happen to me; I'm never going to be accountable for what I'm doing." I think many agnostics and atheists think "well, I can't believe that there's really a God, so probably when I die I'm just gone. But I still care about people, and I'm going to live as if they matter." I think there's more hope for the second kind of person to be reached in some way than the first.
When people speak of everyone being a sinner from birth they aren't normally looking specifically at actions. Rather, they're thinking of sin as the attitudes that lead to wrong actions. If you read the Gospels you'll find that Jesus emphasized intent. He wasn't big on lists of sins, but on things like love, forgiveness, etc. Christians think that people are all imperfect. Even the best actions come from mixed motivations. Thus we all need, and have available, God's grace. I have no idea whether God will consider an infant responsible for any specific action they've done. But I do think they are just as much in need of God's grace as an adult, and like an adult, it is available to them. (In fact most Christians think that all infants are saved, but by a special act of God's grace, and not because they are sinless.)