Learn Croatian: Dječak je protrčao kroz dvorište. - The boy ran through the courtyard.

The prefix pro- here indicates transit through a space. While trčati simply means "to run", the perfective verb protrčati specifically means "to run through" or "to run past" something from one side to the other.

Why do we use both the prefix pro- and the preposition kroz here? Isn't that redundant?

It might feel redundant, but it is a standard pattern in Croatian. When a verb uses the pro- prefix to show motion through a space, it is frequently paired with kroz (through) to explicitly link the action to the physical location.

Could I just use the imperfective verb trčao here instead of protrčao?

You could say Dječak je trčao kroz dvorište, but the focus changes. The imperfective trčao highlights the ongoing action, like he was spending time running around inside the courtyard. The perfective protrčao means he quickly crossed the courtyard and exited, treating it as a single completed trip.

What case is dvorište in, and why does it look unchanged?

It is in the accusative case because the preposition kroz always triggers the accusative. Because dvorište is a neuter noun, its accusative form looks exactly the same as its nominative dictionary form.