Learn Turkish: Düşman savaşçılar antik şehri istila etmiş olsa gerek. - Enemy warriors must have invaded the ancient city.

The suffix -meli is primarily used for obligation ("should" or "have to"). While it can sometimes imply assumption, strong logical deductions about the past ("must have done") are formally constructed with the evidential past -mIş followed by olsa gerek (literally "it is necessary that it be").

Why is şehir written as şehri here?

Two things are happening. First, şehir takes the accusative suffix -i because the ancient city is the specific direct object of the verb istila etmek (to invade). Second, şehir is one of several two-syllable words that drops its second vowel when a vowel-starting suffix is added, transforming it from şehiri to şehri.

The subject is plural (savaşçılar). Why don't we add a plural suffix to the verb structure, like istila etmişler olsa gerek?

In Turkish, when a third-person plural subject is explicitly stated in the sentence (especially if they are human, like savaşçılar), making the verb plural is entirely optional. It is very common and natural to leave the verb in the singular form as done here.

Could I say istila etmiştir instead of istila etmiş olsa gerek?