Learn Farsi: مدیر شرح منحصربه‌فردی را می‌خواند. - The manager is reading a certain unique description.

This is the exact pattern for a specific indefinite object. The -i makes it "a" description (not "the" description), but adding râ shows that the speaker has one specific, real description in mind. It translates best as "a certain unique description."

Where does the indefinite "-i" attach when there's an adjective modifying the noun?

It attaches to the very end of the noun phrase. Instead of putting it on the noun شرح (description), you link the noun and adjective with an invisible ezafe (sharh-e) and add the -i to the adjective منحصربه‌فرد (unique), resulting in sharh-e monhaser-be-fard-i.

The word "monhaser-be-fard" looks like it's made of multiple words. What is its literal breakdown?

You are right! It literally means "restricted to the individual." It is made of منحصر (exclusive/restricted), the preposition به (to), and فرد (individual/single). In modern Farsi, it is treated as a single compound adjective meaning "unique."

How do we know if "mi-khânad" means "reads" or "is reading"?

Farsi uses this same present tense form for both habits (present simple) and ongoing actions (present continuous). You have to rely on context. Because the manager is interacting with "a certain" specific description here, it strongly implies an action happening right now ("is reading").