Learn Farsi: اینجا سیگار نکش، من بیمار هستم.

This is the negative imperative you are learning in this lesson! The full verb for smoking is سیگار کشیدن. The present stem of کشیدن is کش (kesh). To tell someone not to do it informally, we add the negative prefix نـ (na-). So, نـ + کش = نکش (nakesh).

The word سیگار means cigarette, but what does the verb part literally mean?

The infinitive verb is کشیدن (keshidan), which literally means "to pull" or "to draw". In Farsi, you do not use a specific standalone verb just for smoking; instead, you say you literally "pull a cigarette".

Do I need to add the pronoun تو to say "you do not smoke"?

No, you can leave out the pronoun تو (you). The command form نکش already implies that you are giving an order to a single person informally. You would only add تو if you wanted to strongly emphasize who you are talking to.

I remember learning مریض for sick. Is بیمار the same thing?

Yes! You might remember مریض (mariz), which is a very common word for sick. Both بیمار and مریض mean the same thing, though بیمار is slightly more formal and is the root word for hospital (بیمارستان). You can use either word here.