Learn Farsi: چند نفر اینجا زندگی می‌کنند؟

This is the golden rule of counting in Farsi: after numbers and quantity words like chand (how many), the noun is always singular! So, you are literally asking "how many person".

If nafar is singular here, why does the verb end in -and (the plural "they" form)?

Even though the noun after chand stays singular in its form, the overall meaning of "how many people" is plural. Because you are asking about a group of multiple people, the verb matches this plural meaning and takes the "they" form.

Is nafar the only word I can use for "person" here?

Nafar is the standard counting word used specifically for human beings. Farsi has other nouns for a person or human, but when you are counting them or asking how many with chand, you almost always use nafar.

How does the verb zendegi mikonand work?

It is a compound verb! Zendegi means "life", and mikonand is "they do". In Farsi, "to live" is literally expressed as "to do life". The mi- part of the verb shows it is an ongoing present action.