Learn Croatian: Moramo izaći kroz glavni izlaz. - We must go out through the main exit.

Since the sentence is about a single, completed action of exiting the building, we use the perfective verb izaći. If we were talking about a habit or an ongoing process (like "we always go out through the main exit"), we would use the imperfective verb izlaziti.

What case does the preposition kroz take, and why don't glavni and izlaz change their endings?

kroz (through) always requires the accusative case. Because izlaz (exit) is a non-living masculine noun, its accusative form looks exactly the same as its dictionary (nominative) form. The adjective glavni (main) simply matches the noun, so it stays the same too.

Is there a connection between the verb izaći and the noun izlaz?

Yes! They both use the prefix iz-, which means "out" or "out of". izaći is the verb for "to go out", while izlaz is the noun for "the exit". You will see this exact same pattern with entering: ući (to enter) and ulaz (the entrance).

Why is izaći in its dictionary form (infinitive) here instead of being conjugated?

It follows the conjugated verb moramo (we must). In Croatian, just like in English, when you combine a modal verb like "must", "can", or "want" with another action, the second verb stays in the infinitive.