Is a prayer valid behind an Imam who makes mistakes in Surah Al-Fatiha (such as saying: "sirat allatheen an'amta 'alayhim" instead of "alladheena," and changing the letter Dad to Zay in "al-Maghdoubi"), or who changes letters in his recitation after Al-Fatiha?

If the Imam replaces the letters 'dhāl' (ذ) and 'ḍād' (ض) with 'zāy' (ز) in Surat Al-Fatihah, and is capable of learning, then his prayer is invalid, and so is the prayer of those behind him. However, if he is unable to learn, his prayer for himself is valid. There is a difference of opinion regarding the validity of the congregants' prayer behind him if they recite Al-Fatihah correctly: some say it is invalid, while others say it is valid with dislike (karāhah).

As for errors (laḥn) outside of Surat Al-Fatihah, they do not invalidate the prayer, even if they change the meaning, as long as they are not intentional.