What is the ruling on taking back one's wife after Khulʿ? And should the three days be spent with her continuously, or alternately with the other wife?

The issue of khul‘ (divorce at the wife’s instance) is based on whether it is an irrevocable divorce or a nullification (faskh). If it is a divorce, it counts towards the number of divorces; if it is a nullification, it does not. The majority of jurists hold that khul‘ is an irrevocable divorce, while others believe it is a nullification, which is the view chosen by Shaykh al-Islam Ibn Taymiyyah.

Based on the majority opinion that khul‘ is an irrevocable divorce, the man would have exhausted the number of divorces, and the woman would not become lawful for him again unless she marries another man and he divorces her after consummation. However, if it is said that khul‘ is a nullification, he may remarry her with a new contract.

Whoever marries another wife is required to spend three nights with her if she is a thoyyib (a woman who has been previously married).