What is the ruling on someone afflicted with obsessive doubts who repeats the opening takbeer until the Imam bows, so he says the takbeer, then recites Al-Fatiha quickly and bows before the Imam rises from his bowing? Is this action correct, or are obsessive doubts not an excuse for abandoning Al-Fatiha? And is it obligatory to repeat the prayers he performed while doubting this action?

The cure for obsessive thoughts (waswas) is to disregard and ignore them. The action mentioned is incorrect. The prescribed action, if you have made the opening takbir and the Imam has already bowed, is to follow him in bowing. Do not occupy yourself with recitation, and consider that rak'ah valid. The prayer is sound and does not need to be repeated. It is permissible for the one afflicted by waswas to adopt the view of those who believe that Surah Al-Fatihah is not obligatory for the follower, in order to repel the waswas and alleviate hardship.