What is the expiation for someone who made many vows during a period of obsessive thoughts, the number of which he does not know?

It is advisable to disregard obsessive thoughts (waswas). A person afflicted with waswas who cannot repel it is like one who is coerced, and no vow is binding upon them. Nothing of what you mentioned is binding upon you, for vowing fifty prostrations is not legislated and is invalid. Similarly, vowing a single prostration without a cause is, according to the sound opinion, also invalid. Prostration of thankfulness (sujud ash-shukr) is a single prostration performed upon the renewal of a blessing or the warding off of an affliction. Al-Nawawi mentioned that vowing a solitary prostration is not binding because it is not an act of worship (qurbah) without a cause.