Is the prayer of a follower of the Hanbali school permissible if he makes a mistake in Al-Fatiha without correction, while the Imam bears the responsibility of reciting it on his behalf?

The cure for misgivings is to turn away from them and not pay attention to them. You should recite in a normal, natural way, and not pay attention to the illusions with which Satan tries to convince you that you have made a mistake in your recitation. Continue your recitation without caring about any of that. Your prayer is valid as long as you do what is prescribed for you, which is to resist misgivings and strive to get rid of them. And as long as you do not intentionally make a mistake in recitation, and you are not absolutely certain that you have made a mistake that changes the meaning, then your recitation and prayer are valid, even according to those who deem recitation obligatory for the one praying behind the Imam. We advise you not to abandon recitation behind the Imam, especially in what the Imam recites silently. Rather, recite and resist misgivings and strive to get rid of them.