Learn Farsi: نویسنده‌ی سرشناس در تهران متولد شد.

To maintain the formal, biographical tone of this sentence, you would replace نویسنده‌ی سرشناس with the formal 3rd-person singular pronoun وی (vey). It would become وی در تهران متولد شد. This is much more appropriate for written text or journalism than the everyday pronoun او (ou).

How does the compound word سرشناس (sarshenas) literally translate to "prominent"?

It combines سر (head) with شناس (the present stem of شناختن, meaning to know or recognize). Think of it as describing someone whose head stands out and is easily recognized in a crowd.

As a spelling refresher, why is there a ی added to the end of نویسنده (nevisande)?

Because نویسنده (author) ends in a silent ه that makes an "e" vowel sound. When you link it to the adjective سرشناس using the ezāfe grammatical connector (which is also an "e" sound), Farsi requires the consonant ی (y) to bridge the two vowels, making it pronounced nevisande-ye.

The formal verb متولد شد (motavalled shod) is used here for "was born". What is the conversational equivalent?

While متولد شدن is very common in written Farsi and formal speech, everyday casual conversation almost always uses به دنیا آمدن (to come to the world). In casual speech, you would say او در تهران به دنیا آمد instead.