Is the fast valid for one who intended to fast absolutely without specifying the type of fast, and is it obligatory to restart the expiatory fast from the beginning?

Dismiss the intrusive thoughts and do not heed them. If you intended to fast the two months at the beginning of your fasting, then that suffices you, and you are not obliged to repeat it. This is because many scholars have made concessions regarding the intention, holding that a single intention is sufficient for consecutive fasting, as maintained by Zufar, Malik, and in one narration from Ahmad. Since you are afflicted with intrusive thoughts, you are permitted to adopt this view. However, if you did not intend at the beginning of the month, then ignore this intrusive thought and proceed with your fasting, and do not indulge it.