All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, you should know that you have committed a grave major sin by establishing a relationship with a woman who is not your wife, and this is even more abominable because she is still married [she has a husband]. If you committed adultery with her, then this is another grave sin added to what you had already committed. Moreover, speaking to her about marriage while she is still married to her husband is considered as spoiling her marital relationship with her husband, and this is also a forbidden matter. Therefore, you should separate from her and sincerely repent to Allaah from all these sins. For more benefit on the conditions of repentance, please refer to Fataawa 86527 and 87903. Also, for more benefit on the prohibition of spoiling the marital relations between a woman and her husband, please refer to Fatwa 92056.
The fact that this woman had already sent to her husband the papers of Khul’ so that he would sign them, does not mean that the Khul’ took place, because for Khul’ to take place, the husband should agree to it.
Even if we presume that Khul’ had taken place, it is not permissible for this woman to remarry until the expiry of her waiting period. The waiting period of a woman in Khul’ is like the waiting period of a divorced woman according to the preponderant opinion of the scholars so she should observe three menses; for more benefit, please refer to Fataawa 93593 and 92487.
As regards this child (with whom she is pregnant), you have no relation with him/her, and it is absolutely not permissible to trace him/her back to you. Rather, he should be traced back to her husband because he is her/his father, and the child cannot be denied from his father unless he denies him by Li’aan.
Li’aan is when the husband and the wife invoke the curse of Allaah on the liar amongst them when the husband accuses his wife of having committed adultery. Indeed, this husband should deny this child with Li’aan since he knows for sure that it is not his child, and in this case, the child is born out of illegal sexual intercourse.
Allaah Knows best.