I will reply to your post in stages as it is now too long for a single reply.
The usage of the word begotten
You said
This is what Irenaeus' says "Against Heresies" Book 3, Ch 9,
"On the other hand, He [i.e. Jesus] says, "He that believeth not is condemned already, because he has not believed in the name of the only-begotten Son of God;" that is, he separated himself from God of his own accord."
So it is evident that Irenaeus associates the word "begotten" with the incarnation, and not with the "eternal generation" of the Word.
First, I'm going to correct your reference--you were citing from Book 5, chapter 27.
But, be careful here--the "he" in the part you underlined does not refer to Christ, but rather to the nonbeliever. See the preceding lines:
But on as many as, according to their own choice, depart from
God,
He inflicts that separation from Himself which they have chosen of their own accord. But separation from God is death, and separation from light is darkness; and separation from God consists in the loss of all the benefits which He has in store. . .
It is in this matter just as occurs in the case of a flood of light: those who have blinded themselves, or have been blinded by others, are for ever deprived of the enjoyment of light. It is not, [however], that the light has inflicted upon them the penalty of blindness, but it is that the blindness itself has brought calamity upon them: and therefore the Lord declared, He that
believes in Me is not condemned,
John 3:18-21 that is, is not separated from
God, for he is united to God through
faith. On the other hand, He says, He that
believes not is condemned already, because he has not
believed in the name of the only-begotten
Son of God; that is, he separated himself from God of his own accord.
I'll point out that additionally, in Book 2, Chapter 13, paragraph 8, he says the following:
Just as he does not err who declares that God is all vision, and all hearing (for in what manner He sees, in that also He hears; and in what manner He hears, in that also He sees), so also he who affirms that He is all intelligence, and all word, and that, in whatever respect He is intelligence, in that also He is word, and that this Nous is His Logos, will still indeed have only an inadequate conception of the Father of all, but will entertain far more becoming [thoughts regarding Him] than do those who transfer the generation of the word to which men gave utterance to the eternal Word of God, assigning a beginning and course of production [to Him], even as they do to their own word. And in what respect will the Word of God— yea, rather God Himself, since He is the Word — differ from the word of men, if He follows the same order and process of generation?
Here we see that St. Irenaeus both explicitly calls Christ eternal, and identifies Him as God Himself. But as you have rightly pointed out, elsewhere, He is not the same Person as the Father.
381 AD Version
And in one Lord Jesus Christ, the
only-begotten Son of God, begotten of the Father
before all worlds (æons), Light of Light, very God of very God, begotten, not made, being of one substance with the Father;
I will note here that
aeons can also mean "ages", and this is how it's normally translated; hence our English word, "eons".
The 381 version clearly utilizes the word begotten to infer the eternal generation of the (heavenly situated) "Son" (i.e. Logos), whereas in the 325 version it is still possible to conceive the word "begotten" in the Irenaean sense of the incarnation (i.e. separation of the Word from the Father), despite the "begotten not made" phraseology. Yet the Irenaean meaning is inherently strained in both versions of the Nicene Creed, given that as regards to his body, Jesus was "made" in the same way as anyone else, i.e. in the womb. That is to say, Jesus was both begotten and made.
I think you're misrepresenting St. Irenaeus. He explicitly argues against those who would espouse a non-eternal begetting of the Son from the Father.
Even Catholicism says that Jesus had a rational, human soul, inferring that his body was made for him, but (as an aside) I tend to think that there was much more in Apollinarius of Laodicaea's observation than is generally acknowledged, i.e. that the soul of Christ was divine and of the Logos due to his supernatural conception.
The corollaries of the Catholic and presumably Orthodox interpretations are that by saying that Jesus had a human soul, they are then forced to adopt a dyophysite view of Christ by saying that his human nature was unified with the divine nature, whereas the Apollinarius conception has his human rational soul being fully divine (as to origin), although limited by his humanity.
It's my understanding that Apollinarius claimed Christ to not have a human mind, soul or will at all, but rather that these things were replaced by Christ's divine Nous.
So it is seen that the "begotten not made" phraseology of the Nicene Creed, at least in 381AD and very likely also in 325AD (but depending on interpretation), does principally infer "generation" of the Logos from God the Father (before all aeons), and so also does suggest a semi-Arian approach,
Not true. Semi-Arianism says that Christ is of a different nature from the Father--similar, but still definitely different.
Whereas the Irenaean "orthodox" usage of begotten denotes only the begetting of the human Jesus and the separation of the Word from the Father i.e. the "Word becoming Flesh."
Again, I'm certain you're misinterpreting Irenaeus, but feel free to post further citations from him if you'd like to suss out what he's getting at. I will admit that Against Heresies is not monkey barrels of fun to read.