Is a marriage contract considered valid if it was concluded between a man and a woman after an illicit relationship, and an Imam and witnesses (five people) were present, but without the prior consent of the parents who live in another country, knowing that they later forgave them and the relationship became good? And what should be done in this case?

The marriage contract must be renewed in the presence of the wife's guardian (wali) or his representative, because the first contract is invalid due to the absence of a guardian, and "there is no marriage without a guardian." Your living together now is unlawful. The contract can be rectified by telephoning the wife's father, so he says: "I give you my daughter so-and-so in marriage," and you respond: "I accept," in the presence of two witnesses who can identify the father's voice. As for the children, they are attributed to you because you believed the contract to be valid.