Is the prayer of the Imam and the congregants valid if the Imam mispronounced the letter "raa" in "Ar-Raheem" from Al-Fatihah, then repeated the verse to correct it before stopping out of fear of hardship for the congregants, and then repeated the prayer individually?

It is clear that the questioner is afflicted with waswasah (obsessive whispering). He should recite in a normal manner and should not repeat the recitation unless he is certain of an error. Do not succumb to waswasah, as it leads to great evil. The prayer is valid and does not need to be repeated. One should turn away from waswasah regarding intention and sincerely devote all actions to Allah the Almighty.