What is the ruling on fasting the two months of Ramadan which the questioner intended to include within a year of fasting, being ignorant of the religious ruling? And do Mondays and Thursdays fall within the fasting of this year, or are they separate from it, taking into account that he broke his fast on very few days throughout the year?

Whoever makes a clear covenant with Allah to obey Him is obligated to fulfill it. So, if someone vows to fast a specific, consecutive year, he must fast all of it consecutively, with the exception of the days of Eid, Tashreeq, and Ramadan. These days are not included in the vow, and there is no make-up for them unless he intended to make them up, and he may break his fast on these days for reasons other than the vow. If he breaks his fast during the days of the vow without an excuse, the continuity is broken, and he must resume fasting. As for fasting on Mondays and Thursdays, these are included in the fasting of the specified year, and after completing it, he is obligated to fast them for life.