Is the prayer valid behind an Imam who does not recite Surat Al-Fatiha correctly, for example, by pronouncing the letter Nun with a Damma in {Ar-Rahman} (the Most Gracious) or the letter Ha with a Damma in {‘Alayhim} (upon them), while there is someone else present who recites better?

The esteemed one to lead the prayer for Quran recitation is the one who recites best. Therefore, whoever does not recite Al-Fatihah well should not be put forward, based on the Prophet's (peace be upon him) saying: "The most knowledgeable of the Book of Allah among the people should lead them in prayer." And the dammah on the letter Haa’ in (عليهم - 'alayhim) is a correct and established recitation, whereas the dammah on the letter Noon in (الرحمن - Ar-Rahman) is an error that does not invalidate the prayer.