Learn Farsi: اتاقی که در آن دعا می‌کند، برای نشنیدن آشوب بیرون است. - The room in which he prays is for not hearing the outside chaos.

You form a negative infinitive by adding the negative prefix نـ to the standard infinitive, turning شنیدن (to hear) into نشنیدن (not to hear / not hearing). Because infinitives act as nouns in Farsi, they naturally follow prepositions like برای (for) to express purpose, just like gerunds do in English.

Is there an Ezafe between نشنیدن and آشوب?

Yes, it is pronounced as na-šenidan-e āšub. When an infinitive or verbal noun takes an object, that logical object is connected to it using an Ezafe. You can think of it literally as "the not-hearing of the chaos."

What is the function of the -ی suffix at the end of اتاقی?

This is the restrictive ی. While it looks identical to the indefinite ی (meaning "a" or "an"), here it attaches to the noun right before the relative pronoun که to single out that specific item. It changes the meaning from "a room" to "the specific room that..."

Why does the sentence use که در آن instead of just translating "in which" directly?

Farsi grammar does not allow prepositions to attach directly to the relative pronoun که. Instead, you must use a resumptive pronoun inside the clause. So, "the room in which he prays" literally must be phrased as "the room that he prays in it" (اتاقی که در آن دعا می‌کند).