What is the ruling regarding the children of a deceased man whom he fathered from a marriage contracted without the knowledge of the wife's guardian, and do they and their mother inherit, especially since the court had not ruled on the divorce case before his death?

We can summarize the answer in the following points:

1. The first child (born of Zina): Is attributed to their mother and inherits from her. The father who committed Zina does not inherit from the child. 2. Validity of the marriage contract: Scholars differed on the validity of the contract (the marriage took place in court without a guardian but with two witnesses). The majority hold that it is invalid, while the Hanafis consider it valid. 3. Inheritance of the child born after the contract: The deceased child inherits without dispute, as scholars agree that the child is attributed to the father and inherits from him if the father proceeded with the marriage believing it to be valid, even if the contract itself was فاسد (irregular/invalid). 4. Inheritance of the wife: The wife does not inherit in an irregular marriage according to the majority of scholars. However, Imam Malik holds that she inherits in a disputed marriage if one of the spouses dies before the annulment of the contract. 5. Reference for ruling: The matter of whether the wife inherits or not should be referred to the court.