Learn Farsi: بعد از آن جنجال بزرگ، او شبانه‌روز در اتاق خود گریه می‌کرده است. - After that big controversy, he allegedly used to cry in his room day and night.

This is the Evidential Past Continuous. The prefix mi- shows the action was continuous or habitual in the past ("used to cry"), while the past participle plus ast ending (-eh ast) adds the evidential layer. It tells the listener that the speaker didn't witness the crying directly, but inferred it or heard about it from someone else (hence "allegedly" or "apparently").

Would it be wrong to just say گریه می‌کرد in this sentence?

It wouldn't be grammatically wrong, but it would change the meaning. گریه می‌کرد is the regular Past Continuous. Using it would imply the speaker knows for a fact that he cried, probably because they were there to witness it. The evidential form گریه می‌کرده است specifically distances the speaker from direct knowledge of the event.

Why use اتاق خود instead of adding the possessive ending to make it اتاقش?

Both are perfectly correct, but خود (self) acts as a reflexive pronoun referring back to the subject (او). Using اتاق خود emphasizes that it was his own room, and it sounds slightly more formal or literary. In everyday speech, you will hear اتاقش more often.

What is the exact breakdown of the word شبانه‌روز?

It is a compound word made of شب (night) and روز (day), linked by the suffix ـانه (-âneh). While it literally means a 24-hour period, it functions here as an adverb of time meaning "around the clock" or "day and night."