Is what happened—thinking to oneself about divorce, or imagining it happening, or doubting it during prayer, sleep, and wakefulness—considered a divorce, and does it invalidate the prayer?

If you suffer from obsessive-compulsive disorder (OCD), your divorce does not take effect. Since the wife being under the husband's عصمة (bond of marriage) is a certainty (yaqin), it can only be invalidated by a certainty of equal measure, and doubt does not remove certainty. Therefore, we advise you to ignore these obsessive thoughts and pay no attention to them, as that is the best treatment for them. If you surrender to them, they will increase and make your life miserable.