What is the etymology of metanoia

rafaella wrote:So there is no correct translation of the expression after all, only paraphrases as I used them in my contribution.

There are already; small excerpt from Wikipedia (but this is also what every etymological dictionary says):
The Greek word used in the New Testament with Busesis translated is μετάνοιαmetanoia, from νοεῖνno no, "think"and μετάmeta, "around"or "to", literally something like: "Rethinking, change of mind, reversal of thinking".
So the term can also be expressed in one word.
Lets move on:
The Hebrew term thrust, who in the Septuagint with metanoiais translated, includes a return to God not only in thinking but in the whole of existence, which includes the change of behavior above all, but also obedience to God, new trust in him as well as the turning away from all evil and anti-divine human inclinations and weaknesses .
Into Latin became metanoiaWith paenitentia, "Repentance, penance", translated, often abraded to poenitentiaand inappropriately derived from poena, "Punishment".
In German, the word Busesused that linguistically with bass, betteris related and original "Benefit, advantage"means. So it signified the satisfaction of the sinner towards God. Luther again emphasized the "horror and believing repentance", from which the current (untheological) meaning "externally imposed punishment or reparation that is independent of the inner attitude" develops.
So one can easily see that the Roman Church by using the word paenitentiathat loudly slipped over quickly poenitentia, affected the difference.
But that already happened in Orthodox times.

rafaella wrote:It is strange that after so many years of Christianity in the West (first Orthodox, then deviating from the true path) there are no correct translations for basic terms.

Is not it; Even in the times of Europe as a whole, there were different interpretations of certain terms. One was never totally in agreement on everything. Even after the councils, and things existed in parallel.
After the schism, the fronts of today have formed over time.
It is actually not realistic to interpret the conditions from then with the orthodox view of today, since that does not reflect the true conditions.

rafaella wrote:But wouldn't the expression repentance be more correct than repentance? Because, as already said, does the word repentance suggest paying for a sin rather than inner pain and repentance for one's own actions (as well as repentance, of course), as does the word metanoia?

As you can see above, in Latin you only have the word with Paenitentiatranslated which means repentance and only in the course of time has the term, due to the similarity of sounds, changed into penancePoenitentia) transformed.
That's just how it was.
It is best to translate the term to people first and then explain to the Orthodox what it means.
E.g. like this:
In the Orthodox Churches, metanoia is primarily understood to be a change in attitude to life, which comes about through the voluntary cooperation of the Holy Spirit on the one hand and the individual on the other. The aim is to accept God's forgiveness, to leave anger against God and fellow human beings behind, and thus to move from an unnatural, inhuman "death attitude" to a natural, human attitude to life. The world spoiled in the Fall, however, pulls man again and again in the wrong direction, contrary to his actual nature as an image and likeness of God, so that metanoia is a lifelong effort against one's own spiritless followers. The mysteries (sacraments) as well as fasting and prayer help by presenting a counter-image to the fallen world in the "here and now".
Source: (by far the best of all wiki articles I've read in several languages)
LG Songul