Book is singular so it's "bog". If it was plural it would be "boger", I believe.
So what does the Danish sentence mean ?
Can this be understood as 'in which language are you writing your book?' as well? If not, what's the meaning?
This is a really strange sentence in English. If we were inquiring about an author's methods, we would say "how do you go about writing your books?" or "how did you write your book?" and then follow it up with a more specific question. If we wanted to know whether a writer used a pencil or a typewriter or computer, we would say "what do you write with?"
I think this translation needs work, as it isn't a literal phrase you could use in English, as it stands - is it a colloquial or literary reference? Could it mean "how is your book writing progressing?" or with an implied omitted word "Are you enjoying writing your book?"
"Did" would also be a good solution, as it invites an autobiographical answer.
If you asked me, "How do you write your book?" in English, I would say, "With a pencil, silly - now stop bothering me while I'm writing."
I interpreted it as "How are you writing your book?". Are you typing it on a computer? Writing it with pen and paper? Writing a chapter a day? I see it as asking what your process, not really focusing on the progress.
I agree. I tried to form this in a way it would actually be said in English such as "how goes your book writing?".