Is it permissible for me to marry my wife with a new marriage contract, after I divorced her three times, and a sheikh issued a fatwa that the third divorce did not occur, while the judge ruled that all three divorces occurred? And can my wife marry another man in a "tahlil" marriage, knowing that we live in an Arab country that only recognizes official documentation?

If the Shar’i judge rules that a triple divorce has occurred, then no fatwa contradicting it is permissible. In this case, the wife has become irrevocably divorced (baynunah kubra), and she is not lawful for her husband until she marries another husband willingly, and he divorces her or dies. It is not permissible to conduct a fake marriage contract (nikah suri) for the purpose of making her lawful (tahlil), as it is invalid and forbidden by Sharia, and its perpetrator is cursed. Both spouses must fear Allah and abide by the court’s ruling. If the court insists on the divorce ruling, then she is not lawful for him until she marries another husband with sincere intention.