Is it obligatory to fast the vowed days due to returning to a specific sin, or is there another expiation, knowing one is capable of fasting? And does the obligation to fast 9 days continue every time the sin is repeated? What is the ruling on one who has a vow to fast but has not fasted until Ramadan arrived?

Merely intending to fast is not considered a vow (nadhr), for a vow is only established by an utterance that signifies commitment. The wording does not necessarily have to be the word "nadhr"; rather, it can be established by any wording that implies commitment, such as "Lillahi alayya kadha" (Upon me for Allah is such and such). If you did not utter words that signify a vow, then fasting is not obligatory upon you. However, if you did utter such words, then it is a vow of obstinacy (nadhr lajaj), and you are given the choice between fulfilling it or offering an expiation for an oath (kaffarat yamin).