Does the husband's statement, "I affirm in this record that she is divorced from me," after the wife waives her legitimate and financial rights during a family dispute resolution session, constitute an irrevocable divorce, and what are the wife's resulting rights?

If a divorce occurs in exchange for the wife waiving her rights, then it is an irrevocable divorce, considered a type of Khulʿ (dissolution of marriage initiated by the wife). This forfeits the wife's right to the dower (mahr) and maintenance (nafaqah). However, it does not forfeit rights that belong to Allah Almighty, such as the right to housing (according to those who affirm it), nor rights that belong to others, such as custody (hadhanah), as it is a right of the child. It is advisable to consult the Sharia court regarding such matters.