"I am writing in this book."
Translation:Ebbe a könyvbe írok.
"Ebben a könyvben írok" would mean that I am somehow in the book and I'm writing there. But you could say "Ebben a könyvben arról olvastam, ..." -- "In this book I read about..."
"Ebbe a könyvbe írok" is literally "I write into this book". Your words "move into" the book.
Basically, when talking about writing, use "ebbe a könyvbe" and never "ebben a könyvben".
Just a little note. You could talk about what the author has (already) written in the book.
"In this book he writes/talks about his life."
"Ebben a könyvben az életéről ír."
But, again, this is something that has already been written in the book. The author is "in the book". Literaturally.