Does a divorce take place if a teacher passes a student who inwardly swore to divorce his wife if he were to pass him? And must he resign to avoid that?

You are not permitted to fail a student who has passed an exam. Rather, give him the grades he deserves so that you do not wrong him. The divorce of one afflicted by waswas (obsessive whispering) does not occur unless explicitly uttered. The cure for waswas is to completely ignore it, disobey Satan, act upon the fatwa you have been given, and follow the directions of trustworthy doctors. A wife must obey her husband and cease working in mixed-gender environments. If she refuses, she is considered nashizah (rebellious). It is forbidden for her father to incite her to rebellion. It is advisable to seek help from sensible people to resolve the issue, or to refer the matter to a judge. If cohabitation with the wife becomes impossible, then divorce her. You have the right to refuse divorcing her until she offers you compensation to redeem herself. Strive to raise and care for your children. The mother's custody rights are forfeited if she remarries or if there are legitimate religious impediments.