Which is more correct: the word "اختلافهم" (ikhtilāfihim) with a ḍamma on the fāʾ and hāʾ, or with a fatḥa on the fāʾ and hāʾ? And what is the reason for that?

In the phrase "اختلافهم على أنبيائهم" (ikhtilāfuhum/ikhtilāfihim 'alā anbiyā'ihim - their differing with their prophets), both the nominative case (raf') and the genitive case (jarr) are permissible. The nominative case involves a damma on the letter hā' (ـهُمُ), while the genitive case involves a kasra on it (ـهِمِ). There is no linguistic basis for a fatḥa on the fā' (ف).

Both cases (nominative and genitive) align with the narration: "أهلك الذين من قبلكم كثرة مسائلهم واختلافهم..." (Those before you were destroyed by their excessive questioning and their differing...). In this narration, the nominative case (ikhtilāfuhum) would be a conjuction (atf) to "كثرة" (kathratu - excessive), and the genitive case (ikhtilāfihim) would be a conjuction to "مسائلهم" (masā'ilihim - their questioning).

However, in the narration: "هلك من كان قبلكم بكثرة مسائلهم" (Those before you perished due to their excessive questioning), the genitive case "اختلافهم" (ikhtilāfihim) is the only determined possibility.