"Sir, are you writing a book?"

The fact that the individual is addressed as 'Sir', implies that it is not a familiar relationship, so Usted is the correct usage, which uses 3rd person.

usted escribe un libro = escribe usted un libro = escribe un libro usted

Present tense (indicative) in Spanish means three things.

Yo hablo inglés: I speak English. I do speak English. I am speaking English.

Yo como pan: I eat bread. I do eat bread. I am eating bread.

Yo vivo en Buenos Aires: I live in Buenos Aires. I do live in Buenos Aires.

Indeed. The question, 'Sir, are you writing a book?' implies that it is an action occurring at the time the question is asked. It's difficult to think of a situation where this question would be asked for an activity which is not occurring at the moment.

In English, we can use the present continuous tense to talk about activities that are on-going, but that we aren't necessarily doing at that moment. However, in Spanish, this is not the case. In Spanish the present continuous is reserved for whatever action you are completing in that precise moment. For example, in English, it would be common to say "I am working at the supermarket," to one of your friends when you are not actually on the clock. But, if you are speaking Spanish and you say, "Estoy trabajando en el supermercado," that would actually mean that you are on the clock working at that moment. Check out LightSpeedSpanish on youtube - they have some great videos explaining grammar concepts like this. Their videos are very succint and to the point - about 10 minutes each!

For some reason duolingo is putting in a lot of continuous progressive sentences and asking for a present indicative answer!

Perhaps it's trying to teach you that, although the tenses look similar in the two languages, they really aren't.