Regarding How could a woman in an adulterous marriage have the right to remarry after a divorce? I believe there is something very important you are missing. Matthew was written to a Jewish readership, Mark and Luke were written for a Gentile readership. As you know from the nativity story, Joseph was betrothed to Mary. Their marriage had not yet been consummated. The word fornication means sex before marriage, adultery is a different word. All Jesus is saying in Matthew is that if you find out after betrothal but before consummation that the other party is cheating, then you can break it off and marry someone else. Gentiles didn't do betrothal like the Jews (the Jews needed a divorce to get out of the betrothal) that is why Mark and Luke do not mention this get-out clause in their gospel, it did not apply to the Gentile situation. In other words, once you consummate a marriage - that's it - you are in it for life, together or separated - but never remarried.
You made assertions, but you did not prove your point from the Scriptures. See: Is a marriage only bound after sex?
God is clear that in the New Testament Law, there are no separate laws for Jews and Greeks. "There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus" (Galatians 3:28). An argument based on a claim that rules for Gentiles are different from Jews is false.
Fornication means sex outside of marriage. It is not always limited to sex before marriage. For example, the man having sex with his stepmother in I Corinthians 5:1 is called fornication, but since she was a married woman it would also be adultery. For definitions of words related to sex from legitimate sources, see Notes on Sex.
The context of Matthew 19:4-6 shows that marriage is under discussion, not engagement.
Evidence that divorce can take place during a marriage is shown in Paul's quote of the Lord: "Now to the married I command, yet not I but the Lord: A wife is not to depart from her husband. But even if she does depart, let her remain unmarried or be reconciled to her husband. And a husband is not to divorce his wife" (I Corinthians 7:10-11), though the divorce being discussed here does not allow for remarriage.