A woman does not have the right to divorce her husband by talaaq. Talaaq can only be issued by the husband. The words in the Qur’aan which speak of issues and ruling of divorce (talaaq) are addressed to husbands, not to wives. Allaah says (interpretation of the meaning): 

“And when you have divorced women and they have fulfilled the term of their prescribed period, either take them back on reasonable basis or set them free on reasonable basis”

[al-Baqarah 2:231] 

“There is no sin on you, if you divorce women while yet you have not touched (had sexual relation with) them, nor appointed unto them their Mahr (bridal-money given by the husband to his wife at the time of marriage)”

[al-Baqarah 2:236] 

“O you who believe! When you marry believing women, and then divorce them before you have sexual intercourse with them, no ‘Iddah [divorce prescribed period] have you to count in respect of them”

[al-Ahzaab 33:49]

 “O Prophet! When you divorce women, divorce them at their ‘Iddah (prescribed periods) and count (accurately) their ‘Iddah (periods). And fear Allaah your Lord (O Muslims)”

[al-Talaaq 65:1]

It was narrated that Ibn 'Abbaas (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “(The right of divorce) belongs to the one who takes hold of the calf [i.e., her husband].” 

Narrated by Ibn Maajah (2081), classed as hasan by al-Albaani in Irwa’ al-Ghaleel (7/108). 

When a husband leaves his wife and she gives him a sum of money in return for that, this is called khula’. This means that the wife frees herself from her husband by returning the mahr or whatever the husband asks for, then he leaves her if he wants to. This is an annulment of the marriage, not a divorce (talaaq). In this case the woman’s ‘iddah is one menstrual cycle. 

This has already been discussed in the answer to question no. 14569. 

Secondly: 

When khula’ is carried out, she becomes a non-mahram to her husband immediately, and it is not permissible for him to be alone with her, and he has no right to take her back, except with a new marriage contract and a new dowry. 

When the ‘iddah – which is one menstrual cycle, or when she gives birth if she is pregnant – is over, it is permissible for her to marry whomever she wants, in accordance with the shar’i conditions of having a wali (guardian) and two witnesses of good character. 

But if the husband has divorced her with a first or second talaaq, it is not permissible for her to go out of her house during her ‘iddah, and it is not permissible for him to throw her out until her ‘iddah is over, whereupon she becomes a non-mahram for him. The reason for that is that perhaps he may decide to take her back, which is what Islam encourages. Allaah says (interpretation of the meaning): 

“And turn them not out of their (husband’s) homes nor shall they (themselves) leave, except in case they are guilty of some open illegal sexual intercourse. And those are the set limits of Allaah. And whosoever transgresses the set limits of Allaah, then indeed he has wronged himself. You (the one who divorces his wife) know not it may be that Allaah will afterward bring some new thing to pass (i.e. to return her back to you if that was the first or second divorce)”

[al-Talaaq 65:1]

During her ‘iddah, it is permissible for her to uncover in front of her husband and adorn herself for him, and for him to speak to her and be alone with her, but he does not have the right to have intercourse with her until after he has taken her back, or he has intercourse with her with the intention of taking her back. 

If the husband has divorced his wife with the last of three talaaqs, or he has divorced her twice or once and her ‘iddah has ended, then she becomes a non-mahram for him and it is not permissible for him to be alone with her, to touch her or to look at her. 

This has been stated in the answer to question no. 21413 and 36548. 

In the answer to question no. 12667 we have explained all types of ‘iddah. 

It should be noted that the ‘iddah of a woman divorced by talaaq who menstruates is three menstrual cycles, not three months. Three months is the ‘iddah for a minor who does not menstruate, or an older woman who no longer menstruates. You will find more information in the answer referred to. 

Thirdly: 

It is not permissible for a woman to go out with non-mahram men or to speak to them over the internet. The evidence for that and the fatwas of the scholars have been quoted in the answers to questions no. 34841, 6453 and 10221. 

Based on this, a woman is not forbidden to wear adornment, perfume, jewellery and other things that are forbidden to the woman who is observing ‘iddah after the death of her husband. Rather what is forbidden to her during the ‘iddah of a revocable divorce is going out of her husband’s house. Going out with men and speaking to them is forbidden in all cases. 

And Allaah knows best.