Re-marriage and reconcialiation after two talaqs and khul' or faskh?

Question

While reading this post After Khul'a: How can husband and wife reconcial -if they want to? I got a new question in mind:

We know that after three times talaq there's no reconciliation. And the husband can only marry his former wife if she had married and legally being divorced by her new husband.

My question is let's assume husband and wife had two times talaq (husband gave two times talaq) before. What happened if there was a faskh or khul' afterwards
_{maybe faskh can only take place if the husband became an apostate or something like that as else I couldn't imagine a good reason for faskh after two talaqs}
will this faksh/khul' count as new talaq or would the talaq "count" will be reset to "0" or put on hold at "2" or what?

Please clarify explaining also whether a reconciliation or marriage would be possible without the wife marrying another man.

Answer 1

Verse (2:229) Divorce is twice. Then, either keep [her] in an acceptable manner or release [her] with good treatment. And it is not lawful for you to take anything of what you have given them unless both fear that they will not be able to keep [within] the limits of Allah. But if you fear that they will not keep [within] the limits of Allah , then there is no blame upon either of them concerning that by which she ransoms herself. These are the limits of Allah , so do not transgress them. And whoever transgresses the limits of Allah - it is those who are the wrongdoers.

And the very next verse

Verse (2:230) And if he has divorced her [for the third time], then she is not lawful to him afterward until [after] she marries a husband other than him. And if the latter husband divorces her [or dies], there is no blame upon the woman and her former husband for returning to each other if they think that they can keep [within] the limits of Allah. These are the limits of Allah , which He makes clear to a people who know.

See in first verse, it is said, if they fear that they cannot keep the limit of Allah then they can separate (means by faksh/khul').

And if that will be counted as the Talaq then next verse will be contradictory, and it will not be saying 3rd time but should be saying 4th time.

The evidence in the verse is clear. Hence the view of Ibn ‘Abbaas RTA was that any separation in which compensation is paid is khula’ and not talaaq, even if the word talaaq is used al-Sharh al-Mumti’ (12/467-470).