Is it permissible to complete the prayer behind an imam who recites "al-Sirat al-Mustakim" (الصراط المستكيم) instead of "al-Sirat al-Mustaqim" (الصراط المستقيم), and am I required to repeat the prayers I performed behind him, knowing that the pronunciation of "qaf" as "kaf" is common in this country, and the imam does not do this in every prayer?

What you are describing might be waswasa (whispering from Satan/obsessive thoughts). We have clarified the rule regarding errors in Al-Fatiha that invalidate prayer, and what is permissible. Some scholars have been lenient concerning the letter Qaf (ق) if it is pronounced resembling Kaf (ك), and they do not consider the prayer invalid on that account. Al-Suyuti, quoting Al-Isnawi, said: "The prayer is valid if one recites (الهمد لله) 'Al-Hamd lillah' with a Haa (ه) instead of a Haa (ح), or (المستقيم) 'Al-Mustaqim' with a 'tied' Qaf (ق) resembling Kaf (ك), because this pronunciation is found in the Arabic language and the meaning remains." We advise you to abandon these obsessive thoughts. If the matter is confirmed, then advise the Imam to correct his mistake. If he is unable to do so, then there is leniency in the matter according to some scholars.