What is the ruling on a person afflicted with obsessive doubts (waswas) who doubts forgetting or adding a pillar, or not having recited parts of the Tashahhud, or the Abrahamic Prayer, or Al-Fatihah, despite knowing that he recited them?

The cure for obsessive whispers (waswas) is to ignore them and not pay attention to them. If you doubt whether you have recited or not, disregard the whisper and proceed as if you have recited. If you doubt whether you missed a pillar (rukn) or an obligation (wajib), dismiss the whispers and assume that you have performed what you doubted about. You should do this with all the whispers that come to you until Allah Almighty grants you well-being.