Is it obligatory to fulfill a vow to fast for a continuous month, given that the vow was made during a period of ignorance of religious rulings, and guidance was found thereafter?

A vow must be fulfilled whenever it is a vow of obedience, and in the manner it was made. So, whoever vows to fast for a consecutive month is obligated to do so. If an excuse arises during his fasting, he may break his fast and then make up the missed days consecutively. However, if he breaks his fast without an excuse, he must restart the fasting.