I keep making the error of "hun leser boken" instead of "leser hun boken". Is the first way even grammatically correct?
Your first one is a regular (grammatically correct) sentence/statement with the verb coming second. The second sentence is a question. Starting sentences with the verb is almost a guarantee for turning it into a question.
Takk! ha en Lingot.
Bare hyggelig! Og takk skal du ha:)
In theinterrogartive sentence the verb preceds the subject
For some reason, "Leser hun boka?" is also correct