Does divorce take place if the wife says, "You are free," and the husband then says, "Yes," bearing in mind that the conversation was normal and the husband had no intention of divorce?

We ask Allah to cure you of these whispers. Your saying to your wife, "You are free," coupled with your answer of "yes," does not constitute a divorce, because it is not an explicit word of divorce (it is an allusive term). An allusive term does not constitute a divorce unless there is an intention, and no such intention was present on your part. As for words of divorce uttered by the wife, even explicit ones, they are of no consequence, because divorce is the right of the husband alone, unless he has delegated the right of divorce to her.