Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
Allah Ta'ala says,
"The divorce is twice, after that, either you retain her on reasonable terms or release her with kindness. And it is not lawful for you (men) to take back (from your wives) any of your Mahr (bridal money given by the husband to his wife at the time of marriage) which you have given them, except when both parties fear that they would be unable to keep the limits ordained by Allāh (e.g. to deal with each other on a fair basis). Then if you fear that they would not be able to keep the limits ordained by Allāh, then there is no sin on either of them if she gives back (the Mahr or a part of it) for her Al-Khul' (divorce). These are the limits ordained by Allāh, so do not transgress them. And whoever transgresses the limits ordained by Allāh, then such are the Zālimūn (wrong-doers, etc.)." (2:229)
According to the Jamhur (majority) which also includes Hadhrat Uthman, Ali and Ibn Mas'ud (Radhiyallahu Ta'ala Anhum) have held that Khula' is Talaq.
Also, the 'Iddat of Khula' is the same as the 'Iddat of Talaq (divorce). The 'Iddat is three months (if not experiencing menses) or three menstrual cycles (if experiencing menses) or till birth (if concieved).
"And divorced women shall wait (as regards their marriage) for three menstrual periods, and it is not lawful for them to conceal what Allah has created in their wombs, if they believe in Allah and the Last Day. And their husbands have the better right to take them back in that period, if they wish for reconciliation. And they (women) have rights (over their husbands as regards living expenses, etc.) similar (to those of their husbands) over them (as regards obedience and respect, etc.) to what is reasonable, but men have a degree (of responsibility) over them. And Allah is All-Mighty, All-Wise." (2:228)
It is the responsibility of the husband to maintain the wife in the period of Iddat. The wife is not permitted to leave home within the Iddah period except in the case of dire necessity.
For more information on Rule of 'Iddah please refer to this link: http://www.askimam.org/fatwa/fatwa.php?askid=30546a7248894caa8d6378b50c6f203e