Is my consent to the illusory marital inventory list, which contained nothing, considered an injustice to the wife, and is she entitled to demand this list after she has requested Khulʿ and repeatedly left the home without my permission?

You made a mistake by signing the exaggerated dowry list, knowing that it is a document that secures the wife's rights. We advise you to seek the mediation of some honorable people to reach a reconciliation for a certain amount of money; otherwise, the court will decide the matter. As for the wife leaving without your permission, its ruling depends on whether it constitutes nushuz (disobedience) or not, and on whether you are providing for her financially.