Is a woman who was married informally and then separated from her husband required to observe the iddah (waiting period), and is it permissible for her to get engaged and be promised marriage by another man during the iddah period?

The marriage is valid if it takes place with the guardian's permission and in the presence of witnesses. Divorce occurs if the husband pronounces it, or if he grants the wife the right to divorce herself and she chooses to do so. If divorce occurs, you are not permitted to marry another man until the 'iddah (waiting period) expires. The 'iddah is obligatory upon divorce, whether pregnancy occurs or not. It is not permissible to explicitly propose to a woman observing her 'iddah. However, it is permissible to make an indirect proposal (ta'rid) to a woman who has been irrevocably divorced (bain) or whose husband has died. The 'iddah observer's statement to a suitor, "I marry myself to you," is not permissible because it is an explicit declaration. A woman is like a man in this regard, noting that a woman cannot marry herself; rather, her guardian marries her off. Patience is necessary, and it is not permissible for a woman to converse with a non-mahram man except out of necessity and while observing Islamic guidelines. The husband has the right to take back his revocably divorced wife. If she dislikes staying with him, she may seek khul' (divorce at her initiative) in exchange for compensation.