Is the prayer valid behind an Imam who does not recite Al-Fatiha properly and alters some words, such as (Saami’ Allahu liman hamidah) instead of (Sami’a Allahu liman hamidah)?

The vernacular pronunciation of the letter Qaf (ق) can alter the letter. Jurists have stipulated that it is impermissible to follow in prayer someone who alters a letter in Al-Fatiha or makes a grammatical error (laḥn) therein that changes the meaning, except for someone who is in the same condition as the imam. Al-Fatiha must be recited with all its letters and emphatic pronunciations (tashdīdāt). Therefore, if someone omits a letter, or lightens an emphatic letter, or substitutes one letter for another while being capable of correct pronunciation, their recitation is invalid.

An illiterate person (ummi) who cannot recite Al-Fatiha perfectly, if they are able to learn, their prayer is invalid, and it is not permissible to follow them. However, if they are unable to learn, their prayer is valid for themselves, and it is permissible for someone in a similar state to follow them.

As for elongating the vowel in "Sami' Allahu liman hamidah" (Allah hears those who praise Him), it appears that this does not invalidate the prayer, but it is a grammatical error (laḥn) that must be corrected. Worshippers should alert the imam to these errors.