As salamu alaykum wa rahmatuLlahi wa baraktuHu,
In the Shafi’i School, a khulu’ counts as a talaq. After khulu’ there is “baynunah sughra,” similar to what happens after a talaq issued before consummation. They may marry again, so long as it was not the third, but only with a new contract fulfilling the normal conditions. A new mahr should be given too. Additionally, housing is obligatory in the ‘iddah but not nafaqah; unless she is pregnant, if she is pregnant nafaqah must be given too. A woman who is nashizah is not entitled to housing. Furthermore, the duration of her ‘iddah will vary depending on her state, like after a normal divorce.
To add, even if khulu’ is given, the wife is still entitled to mut’ah. Imam Shafi’i advised the minimum recommended mut’ah amount to be 30 dirhams.
This is stated in Imam Nawawi’s Rawdah and in Shaykh Muhammad b. Salim b. Hafiz’s al-Miftah Lubab al-Nikah.
And Allah knows best.
Answered by: Shaykh Yaqub Abdurrahman