Learn Farsi: حالا زبان فارسی می‌خوانم.

It follows the standard rule for the present indicative tense: the prefix می (mi-) + the present stem خوان (khān) + the first-person singular ending ـم (-am).

Doesn't the root verb خواندن usually mean "to read"? Why is it translated as "studying"?

Yes, خواندن literally means "to read" (and also "to sing"), but it is very commonly used in Farsi to mean "to study" an academic subject, like a language or a university degree.

The English translation says "am studying," but isn't this just the regular present tense?

Exactly! In Farsi, the present indicative tense (using the می prefix) covers both general habits ("I study Persian") and actions happening right now ("I am studying Persian"). The word حالا (now) makes it clear that it is happening at this very moment.

Why isn't the word for "I" (من) included at the beginning of the sentence?

In Farsi, subject pronouns like من (man) are optional because the verb ending ـم (-am) already tells us who is doing the action. Native speakers usually drop the pronoun unless they want to emphasize it.

How are the words زبان (language) and فارسی (Persian) connected when speaking?