Is it permissible for a Muslim to pray at home if the Imam in his mosque does not recite Al-Fatiha correctly, and the Imam of the next closest mosque is too fast in his prayer, which prevents reverence and the completion of supplications?

Mistakes in reciting Al-Fatiha are of two types: a hidden mistake (Lahn Khafi) that does not invalidate the prayer, and an apparent mistake (Lahn Jali) such as replacing one letter with another, which invalidates the prayer if the Imam is someone who, if informed, would learn. Speed in prayer does not invalidate it if the Imam observes the minimum level of طمأنينة (tranquility/composure). Based on this, one should not abandon congregational prayer unless the first Imam makes an apparent mistake (Lahn Jali) or the second Imam neglects the obligatory طمأنينة.