There is simply too much here to deal with in a single post, at least one anyone would want to wade through. So I'll do a few separate posts. On with the first.
Openness to the supernatural ought to be the natural result of recognizing our limitations. By supernatural we mean what is beyond nature, or more explicitly, what is beyond the physical universe that we are all contained within and a part of. Within the universe we can describe all kinds of relationships and experiences, tangible experiences that indicate objective realities. But the universe gives no explanation for itself. It can't. No self-contained field of relationships can explain its own existence; it can only explain the realities within it. To explain the field itself, reference must be made to something beyond it. As I understand it, this relationship is reflected in the fact that arithmetic, while working fine internally, can not be used to prove its own legitimacy but must defer to algebra to validate it, which then must defer to calculus to validate it. Thus each self-contained field of math is open upwards to levels of reality beyond its nature (super-natural) for its own justification. Likewise, it is the fact that your tangible experiences and the universe they rely on offer no explanation of themselves that ought to lead you to a profound sense of their limitations, which in turn ought to produce an openness upward to a reality beyond the physical universe from which it must derive its meaning. (To clarify, this is NOT the classic cosmological or 'first cause' argument for the existence of God because I'm not here arguing the existence of God, only a basic openness to allow God to reveal himself.)
On the other hand, I think abstract arguments like this are a bit of a dodge and a waste of time. What ought to produce openness to the supernatural is your personal experiences of your limitations, the struggle with your personal nature which we all endure, our inability to fully determine ourselves, to do what we know is right and not do what we know is wrong. It is in our sin that God really finds us, not in our intellectual recognition that he might actually be there.
But even here there is a problem; ultimately it should not be either our abstract reason or personal experience that leaves us open to God, but God himself that opens us up to him. The attitude that demands a reason to be open to this is the very pride and arrogance God must save us from, and judge in the saving. This attitude reduces God to a concept to be considered rather than the Almighty who must be faced. Accordingly, I cannot give you an argument for why you ought to be open to God; the only alternative is to be closed and no truth can come from that.
The claim that taking Jesus' teachings seriously is anachronistic and fails to take seriously the modern scientific world view is faulty because this very claim fails to take seriously the fact that the modern scientific world view changes nothing about Jesus' teaching. Let me say that another way: Jesus' teachings had to do with the relationships of humanity to God, to each other in their personal, political, economic, moral, and familial dimensions, and to the world God has placed us in; he didn't teach physics except the scientifically foundational principle of creation out of nothing, ex nihilo. The progress of modern science can make no judgement on Jesus' teachings because it does not and cannot address them; they have entirely different subject matter, methodology, and authority; the progress of modern science has no corollary in something like a progress of modern morality or civility or culture.
You are formally correct in saying that Jesus never directly addressed himself to atheism; however, materially, Jesus was constantly addressing himself to those who had no real experience of God, giving true objective experience of God in his very presence and address as God. As I've said earlier, he taught his disciples the reality of the kingdom of God and poured out his Spirit on them, enabling them to do the same for others. I am hopeful to do the same for you. In my presence (being on another continent not withstanding) and friendship in the Spirit of faith in Christ, it is my hope that God will open you up to his presence and activity in your life and yours in His. Either way, the reality of millions upon millions of lives who have been changed and brought into contact with the living God up to this very day through the teachings and deeds of Christ read in the Gospels overwhelms your claim of their irrelevance and anachronism.
More to come...