Is Khul’ considered a divorce, and does it mean that only one divorce remains, and is it permissible for the spouses to return to each other after Khul’ twice, and how is that done?

The preponderant view is that khulʿ (divorce at the wife's instance, usually for a consideration paid to the husband) is not considered a divorce, even if it is pronounced using explicit divorce wording. Rather, it is an annulment (faskh) and does not count towards the number of divorces. So, if a man divorces his wife by khulʿ using the word "divorce," it is considered an annulment and not a divorce. Consequently, he has the right to remarry her with a new contract and mahr (dowry), and this does not count towards the number of divorces he possesses. This is the madhhab (school of thought) of Ibn Abbas, Shaykh al-Islam Ibn Taymiyyah, and Shaykh Ibn Uthaymeen, who base their argument on the Holy Qur'an, which differentiated between divorce (ṭalāq) and khulʿ (redemption/ransom).