Has divorce taken place with the word “binaqis” (less) or with the word “lam ya’ud yanfa’” (no longer useful) in the two mentioned cases, bearing in mind that the questioner's intention receded immediately after each word? And does intention in divorce differ from the will to effect divorce?

It appears from the questioner's words that he is suffering from obsessive thoughts about divorce, which is a serious matter. As for the words uttered in the two incidents, they are a 'kinaya' (allusion) of divorce, which depends on the intention of the speaker. If he intended to effect a divorce, it occurs; if he did not intend it, it does not. What seems apparent is that he did not intend to effect a divorce. As for the wife, the advice is to keep her, be patient with her, and treat her kindly, for the Shari'ah encourages keeping one's wife even if disliked, as in the verse: (And live with them in kindness. For if you dislike them - perhaps you dislike a thing and Allah makes therein much good) [Quran 4:19]. And the Prophet, peace be upon him, said: "Let no believing man hate a believing woman; if he dislikes one characteristic in her, he will be pleased with another." However, if one cannot bear to be patient with her, there is no sin in divorcing her.