Learn Farsi: راوی این داستان را برای پادشاه روایت کرد. - The narrator narrated this story for the king.

Yes, they share the same Arabic root. راوی is the active participle (the person doing the action, meaning "narrator"), and روایت is the verbal noun (meaning "narration"). You will often see this pattern in Farsi where a person's title and the action they perform share the same root letters.

The current lesson is about putting reporting verbs before the subject. Why is روایت کرد at the very end of this sentence?

This sentence uses standard Farsi SOV (Subject-Object-Verb) word order, which is the default for general storytelling and everyday writing. The verb-subject inversion you are learning about is a specific stylistic choice used almost exclusively in news media and formal journalistic reporting, rather than standard narrative sentences like this one.

How would this sentence look if we applied the journalistic inversion rule from this lesson?

To apply that style, you would pull the verb to the front to introduce a subordinate clause, looking something like روایت کرد راوی که... (The narrator narrated that...). However, keep in mind that news articles typically use verbs like گفت (said) or افزود (added) for this structure, while روایت کردن is more literary.

Could the phrase برای پادشاه go before the direct object این داستان را?

Yes, Farsi word order is quite flexible with prepositional phrases. You could absolutely say راوی برای پادشاه این داستان را روایت کرد. Placing the prepositional phrase before the direct object is very common and simply places a little more emphasis on the fact that the story was specifically for the king.