I think you are stretching the Greek a little. Here is an actual word for word translation:
And we know that/because He/that One was shown/manifested in order that/ to the sins to bear away. And sin in Him not is.
If you would like I can give you the Greek and the translations of each word.
Now we must look at the 2 conjunctions, Kia, And. They, in both places they are used, connect what was said before with what is being said. Interpretation of the Greek most often relies on the context.
So what was said before in verses 1-4.
1 John 3:1-4 (KJV) 1 Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not. 2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is. 3 And every man that hath this hope in him purifieth himself, even as he is pure. 4 Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law.
There are 3 subjects that the Apostle is pointing to: believers, sin and the Lord Jesus Christ.
First he speaks of who we are in Christ. Then he talks about what should be the outcome of faith in Christ. Then he speaks of what sin is in the objective sense of the word. He is not telling us that sin is only the transgression of the Law, for as Paul tells us in Rom. 14:23 that whatever is not of faith is sin.
Now the word Kai or And that connects the thoughts of sin being a transgression of the Law and our standing in the law in Christ. We are sinless as far as the law is concerned. In Him is no sin. Verse 7, though, really gets to the point of the whole subject of sin and the believer.
1 John 3:7 (KJV) Little children, let no man deceive you: he that doeth righteousness is righteous, even as he is righteous.
Oh is not saying the believer must keep the law for that is impossible. What he is saying is that we no longer walk in this world relishing sin. He is setting up his next statement of fact; that we who are born of God cannot sin.
To answer your points I would say first that exchanging the words as you did is not really a good way to do grammar. The Lord Jesus is where John starts His epistle and is his subject throughout. Everything is in the context of Christ and His work.
Concerning verse 5 you are a little off. The words He and Him are different words in the Greek. The first He is a demonstrative pronoun. The second Him is a simple personal pronoun which is in the Dative case. It is used to express the indirect object of the verb. In this sentence Him would be the indirect object of the verb “is”. Actually Him would be the indirect object of “ not is”. Therefore who or what is the direct subject? Of course it is sin.
Now the whole sentence cannot stand alone. It must be understood in its context to provide the actual expression of thought. So we ask the questions who, what, when and where. Who is John talking about in the context? The answer would be believers since we are the subject from verse 1, well actually from 2:1, though the division of verses is not in the Greek. We are the object of his discourse as can be clearly seen.
He was manifested to take away our sins is the clause that comes before in Him is no sin. Again we find the word and which joins the 2 clauses together. He came to do something and having done it the result is in Him is no sin. It wouldn’t agree with the context to make “Him” be the object of the phrase. John is simply reminding us that in Him we have no sin. He took it away.
I will leave it there. Looking forward to your response. I know that I have made it more complicated than it should be but bear with me.
I am only addressing verse 5 right now. You still have that contextually wrong. The second portion of that verse "in him is no sin" is
NOT talking about a believer. You have taken that portion of that verse out of context.
Let's start with the word "and" (kia) because as you say, it's used both places here: (I'm still talking about verse 5).
Your quote:
"They, in both places they are used, connect what was said before with what is being said. Interpretation of the Greek most often relies on the context."
(This is quoting you; which what you are saying here isn't exactly clear? Except "Interpretation of the Greek most often relies on context.")
If you are saying "and" (kia) is used in two places in verse 5; that is true.
If you are saying "they" is used in both places in verse 5; that is not true.
If you are saying (kia) is somehow related to the word "they" in verse 5; that is not true either.
Kia is translated as: "and" 8,173x; "also" 514x; "even" 108x; "both" 43x; "so" 18x; "likewise" 13x; not translated at all 350x; miscellaneouslly translated 31x
This word "and" (which is a conjunction) connects what is said before, to what is being said. That is true, because that is what conjunctions do.
Conjunctions though do not automatically make the phrases they are connecting, say the same thing as the phrase before them.
For example #1: I am going to the store to buy milk and butter. Of the milk and butter, I am performing the same action. I am purchasing them.
For example #2: I am going to class today and I am selling my science book. Now the assumption is that I'm selling my science book in class, yet "going to class" and "selling my science book" are different actions. It is not the same as the first example, where I am performing the same action. Maybe I'm going to English class and History class and selling my science book at the book fair in the student union.
So "and" in verse 5.
Verse 5 starts with an "and"; which connects it to verse 4. Verse 4 is talking about sin being transgression of the law. "And you know He was manifest to take away our sins..."
Just like the example of going to class and selling the book. Sin is the transgression of the law; connected to this "And you know...(X,Y and Z)." The two phrases are related, but it's not the same action. One action is talking about transgressing the law and the other action is taking about "what you know" concerning what Christ did as it relates to you transgressing the law.
So following what you just said here "And" is connected to the phrase before it: "And you know He was manifest to take away our sins; AND in HIM is no sin" So if "and" is talking about the phrase before, than "in him is no sin"; can only be talking about Jesus. You yourself just made that point!
Now back up to verse 4. Verse 4 was just talking about transgressing the law. You know He was made manifest to take away sins. His relationship to the law is that "in Him is no sin". That is why the second half of verse 5 says that. It is making the point that Jesus was without sin. There is no other way to interpret the second half of that verse without taking it out of context. You are wrong when you say that is referring to believers. That is categorically wrong.
It is not only a wrong interpretation for grammatical reasons; it is also categorically false. "In believers is no sin" is fundamentally a false statement.
Now what you said about "he" and "him" being different Greek words. Why are they different Greek words? You didn't address that. The "he" in these passages is attached to the verb; so of course your Strong's number base is going to be the number of the verb.
The "he" in Greek constructs that are attached to verbs is composed of 2 different Greek words.
One of those words is simply a pronoun "he", "she", "it". It is not gender specific. It gets its gender specifics from the context of the sentence. As you said, context is important.
The other Greek word means "that", or "this" or "one" (that one / this one); which is where we get "dative", "demonstrative", "possessive" pronoun. Something is "dative case" when it is attached to the verb. But "dative" does not negate "demonstrative possessive" either. They are two different terminologies for the same thing.
That "one he" is attached to the verb of what "he" does.
"...that he appears...",
"...that he takes away....",
"...that he sings...",
"...that he - fill in the blank...".
"And...." (your conjunction - which you just said, connects back to the phrase before it) "....in Him is no sin."
So, if you can not admit that your interpretation of the second half of verse 5 is not correct; than there is no reason to continue with this conversation.