The ‘iddah of a woman divorced by khula’ and her going back to her husband
Question

                If a wife asks her husband for a khula and he accepts, how long is the waiting period?Is it irrevocable i.e can they ever re-marry?
Praise be to Allah.
    If the woman who has been divorced by khula’ is pregnant then 
    her ‘iddah lasts until she gives birth, according to scholarly consensus. 
    Al-Mughni, 11/227.

     But if she is not pregnant, the scholars differed concerning 
    her ‘iddah. Most of the scholars said that she should wait for three 
    menstrual cycles, because of the general meaning of the aayah 
    (interpretation of the meaning):

    “And divorced women shall wait (as 
    regards their marriage) for three menstrual periods”

    [al-Baqarah 2:228]

     But the correct view is that it is sufficient for a woman 
    divorced by khula’ to wait for one menstrual cycle, because the Prophet SAWS 
    (peace and blessings of Allaah be upon him) told the wife of Thaabit ibn 
    Qays, when she divorced him by khula’, to wait out the ‘iddah for one 
    menstrual cycle. (Narrated by al-Tirmidhi, 1185; classed as saheeh by 
    al-Albaani in Saheeh al-Tirmidhi, 946). This hadeeth refers 
    specifically to khula’ divorce whereas the aayah quoted above speaks of 
    divorce in general. But if she waits out an ‘iddah of three menstrual cycles 
    that will be more complete and will be on the safe side, and will avoid an 
    area of scholarly dispute, as some scholars say that she should wait for 
    three menstrual cycles, based on the aayah quoted.

    Fataawa al-Talaaq by Shaykh Ibn 
    Baaz, 1/286.

     There is nothing wrong with them remarrying with a new marriage contract. See question no. 10140.