What should one do who vowed to fast ten days without verbalizing the intention, then became strongly certain that he intended to fast them consecutively? And does unknowingly breaking the fast affect a vow fast?

The answer is summarized as follows: The questioner has many intrusive thoughts and is advised to disregard them. If the questioner is certain that he uttered the formula of a conditional vow, and the condition for it was met, then he must fulfill it. However, doubt about the intention of continuity is as if it doesn't exist, and the default is the absence of such intention. Whoever did not intend continuity may fast the days separately, according to the majority of scholars. It is sufficient for the questioner to fast the remaining days separately or consecutively, and he is not required to repeat the five days he fasted non-consecutively. And whoever breaks a votive fast forgetfully should complete the rest of the day and is not required to fast a day in its place.