What is a vow (nadhr), what is the ruling on a specified vow, is it permissible to cancel a vow of fasting in the event of failure and negligence, how can one repent from that, what are the guidelines for repenting from a bad habit, and what about taking one's wife to a non-Islamic environment?

This vow is considered a "vow of contention" (nadhir al-lajaj). If you break it and commit the sin, you must repent for the sin. Then, you have the choice between fulfilling the vow or offering an expiation for an oath (kaffarat yamin (definition)). The apparent meaning of the word "whenever" (kullama) is that the vow is repeated whenever the sin is committed. We advise you to maintain the prescribed supplications (adhkar ma'thurah), increase your remembrance of Allah with a present heart, and ask Him for forgiveness and chastity. Rely on seeking treatment through supplication to Allah, asking Him to rid you of this habit. Increase your recitation of the prescribed supplications such as: "I seek refuge in You from the evil of myself, and from the evil of Satan and his polytheism, and from committing evil against myself or causing it to a Muslim," and "O Allah, I ask You for guidance, piety, chastity, and self-sufficiency," and "O Allah, purify my heart and protect my private parts," and "O Allah, I seek refuge in You from the evil of my hearing, and from the evil of my sight, and from the evil of my tongue, and from the evil of my heart, and from the evil of my semen." We also advise you to read books on encouragement and deterrence (targhib wa tarhib), associate with good people, avoid foods that stimulate desire, occupy your time with productive activities, increase voluntary fasting, and persevere in remembrance (dhikr (definition)).