Is it obligatory to make up prayers that were performed facing the wrong direction after ascertaining the correct direction, and what is the ruling on doubting the making up of prayers for someone afflicted with obsessive thoughts?

Errors in determining the Qibla while in settled areas are not excused by most scholars, as you could have verified the Qibla by looking at a nearby mosque or by asking a trustworthy person.

Prayers that were performed with errors in Qibla determination must be re-prayed. As for the person suffering from obsessive thoughts (waswas), they should disregard the waswas and not pay attention to it. If they doubt whether they have re-prayed or not, they should assume that they have re-prayed.