Here is a rather erudite article on the Greek word ‘metanoia’. Please read it and give me your impressions.
Well, first of all, it is a rather biased way to promote your proposed meaning of a word by quoting a lot of English translations with the word you are trying to prove something about already translated to the meaning you are promoting. While this proves that your meaning can fit in these passages, it does not prove that your meaning is actually the meaning of the word, since you are dependent upon whatever translator you are using.
I teach that metanoia means literally, “after-mind.” To translate it to English in a single word, I would use either “submission,” “yieldedness,” or “easing.” This based on my translation of metanoeo as “to submit,” “to yield,” or “to ease.”
In the example of the Athenian counsel, one of the second two meanings would fit well. They yielded (to pressure to be more lenient,) or eased (the penalty they thought to impose.)
Xenophon yielded his former opinion on consideration of historical facts.
The Dardani yielded.
First the men yielded to the smile of Cypselus, then they again yielded to their orders, but too late.
In I Samuel 15:29, the Lord is not a man that He should yield or submit.
In Proverbs 20:25, it is foolish to dedicate something as holy before you have really considered the cost of submitting it to the Lord.
In Jonah 3:9-10, the Ninevites were hoping the Lord would yield or ease His harsh penalty.
Certainly yes, it was the Latin fathers who saddled the word metanoia with the idea of penance.
In Hebrews 12:17, what Esau sought was submission or yieldedness on the part of his father, but that he did not receive, for Isaac had made his decision, and there was no room for him to relent.
II Peter 3:9 and Luke 5:32 both speak of the need for men to submit.
In Luke 17:3-4, the idea of yielding or submitting is again in view.
In Acts 2:38, we do not know what the people’s former opinion had been of Jesus Christ. Since many were foreigners, they had not necessarily even heard about Him, or had an opinion about Him before. This shows the weakness of forcing metanoia to mean a change of mind, rather than making up the mind. Peter is calling upon these people to submit to the truth they have now heard about Christ, whether or not they had other thoughts about Him before. Some of them might have thought very positively about Him before, and this certainly was not supposed to change.
Acts 17:29-31 is calling upon men to submit to God’s government, rather than what the author suggests, changing their minds about idols and God.
Metamelomai probably does mean regret.