Does divorce take effect with the utterance of "I don't want her" in an inaudible voice, or by an attempt to say "I have divorced her" with a muddled pronunciation, or by saying "I divorc" without uttering the letters ta' and ha'? And is the psychological state that the questioner is experiencing with his wife a justification for seeking divorce without doubts?

What has been mentioned are merely whispers (waswas) that do not result in divorce. Therefore, do not pay attention to these doubts and whispers, and completely disregard them, because divorce is permissible when there is a need for it. However, divorcing one's wife to get rid of the pressure of whispers and doubts is not a sound approach, as Satan wants to create separation between a man and his family. The cure for waswas is to seek refuge in Allah from the accursed Satan, and not to bring about what Satan desires. So, keep your wife and live with her honorably, and do not pay attention to the whispers.