Do the husband's words, "Yes, divorce me, yes, he said to me: you are divorced," which he said to help his wife overcome her obsessive thoughts about divorce, constitute a divorce? And what should the wife do to get rid of her obsessive thoughts about divorce?

Divorce does not occur with such words. It is advised to completely disregard whispers (waswas) and not pay attention to them, to seek Allah's help and supplicate to Him, to frequently remember Him, and to occupy one's time with what benefits them in their religious and worldly affairs.