What is the ruling on the prayer of someone who doubted the correctness of his pronunciation of a letter in Al-Fatiha, then completed his prayer and afterward researched the issue?

Your prayer is valid and is not invalidated merely by doubting the correct pronunciation of a letter from Al-Fatihah. The default is that the prayer is valid, and it is only invalidated if something that invalidates it occurs with certainty, "because the default is the absence of an invalidator." You must ignore intrusive thoughts and not pay attention to them.