Does a woman return to her first husband if he has intercourse with her after the Khul’ without the intention of reconciliation, and is her second marriage valid?

If "she was divorced khul'an" means that he divorced her through khul' or for a financial consideration, then this is an irrevocable divorce (talaq bain) from which there is no return. Both spouses bear a great sin. The woman should have completed her first 'iddah, then observed an 'iddah for the illicit intercourse. If she married before the 'iddah for the illicit intercourse expired, her marriage is invalid according to some scholars. However, others do not require an 'iddah for zina (fornication/adultery). It is advised to present the matter to a Sharia court or to trustworthy scholars.