What is the ruling regarding a wife who lied to her husband after he made her divorce contingent upon her truthful answer or upon her performing a certain action? And how many times does divorce occur if this wording is repeated in the form of "divorced" or "you are divorced"? And does divorce occur in a state of anger?

Your statement to your wife, "You are divorced" (أنت طالق), does not constitute a divorce. As for contingent divorce, the fatwa we follow is that the majority of scholars hold that it occurs if the condition upon which it was made contingent is met, whether the intention was divorce or threat. Furthermore, a divorce pronounced with the word "three" counts as three divorces, contrary to the view of Ibn Taymiyyah. So, if you made the divorce of your wife contingent upon her lying to you three times, and she then lied, the three divorces have occurred, and your wife has become irrevocably separated from you (bainunah kubra). The issue should be presented to a Sharia court or trusted scholars, and we advise against swearing by divorce.