Learn Farsi: نگهبان قدم می‌زد که خش‌خش برگ‌ها را شنید. - The guard was walking when he heard the rustling of the leaves.

In this specific grammatical structure, که acts as a narrative interrupter. When placed between a background action in the Past Continuous (قدم می‌زد, was walking) and a sudden new event in the Simple Past (شنید, heard), it translates to 'when' or 'when suddenly'.

Could I just start the sentence with وقتی که (vaghti ke) to mean 'when'?

You could, but it changes the storytelling focus. Starting with وقتی که simply states two overlapping events. Using که alone in the middle of the two clauses, as shown here, specifically creates a dramatic interruption: he was walking along when suddenly he heard a noise.

How does the verb قدم می‌زد (ghadam mi-zad) break down?

It comes from the compound verb قدم زدن (ghadam zadan), meaning 'to stroll' or 'to walk'. Literally, قدم means 'step' and زدن is 'to hit' or 'to strike'. Here, it takes the continuous prefix می (mi-) to show an ongoing background action.

Is خش‌خش (khesh-khesh) a sound-effect word?

Yes, it is an onomatopoeia mimicking the crisp, rustling sound of dry leaves or paper. Farsi frequently uses double-barreled words for sounds, such as پچ‌پچ (pech-pech) for whispering or چک‌چک (chek-chek) for dripping water.