Is the tyrannical Bāṭinī considered a believing Muslim merely by outwardly professing Islam? Am I required to repeat the prayers I performed behind the preacher who invokes victory for him and describes him as a believer, knowing that I doubt my prayer behind him? And is there any sin upon me if I stop praying behind him and change mosques?

The preacher may be ignorant that the tyrant is a Batinite, or ignorant of the beliefs of the Batinites. Therefore, it is not permissible to judge him with disbelief or his contentment with those beliefs except with absolute certainty. Your prayers behind him are valid and do not need to be repeated. There is no harm in praying behind him as long as he does not commit any of the nullifiers of Islam after the establishment of the proof. You may pray elsewhere if you wish, and the Imam should be advised with gentleness and kindness, and the transgression explained to him with wisdom.