Is it permissible to pray behind an imam who mispronounces Al-Fatiha in obligatory or supererogatory prayers (such as mispronouncing "Ar-Rahman" by opening the "nun" instead of vocalizing it with a kasra), with this mispronunciation recurring despite advice?

Opening the نون (nūn) in the word "الرحمن" (Ar-Rahman) in Surat Al-Fatihah during prayer is not permissible if done intentionally. However, it does not invalidate the prayer because it does not change the meaning. It is disliked to pray behind someone who does this.

If the linguistic error (laḥn) does not change the meaning, then his prayer is valid, and the prayer of anyone who follows him is also valid. But if it changes the meaning, such as pronouncing the letter ت (tā’) in "أنعمت" (an‘amta) with a dhammah (an‘amtu) or a kasrah (an‘amti), or if it invalidates the meaning, then if his tongue is capable and he can learn, he is committing a forbidden act and must hasten to learn. If he falls short and time is limited, he must pray and make up (the prayer), and it is not permissible to pray behind him.