Woah... His backroom is kinda awesome!
So yeah, our theory's about Inky seem to be correct. It converts normal books into the book that the customer needs, and turns them back when the customer leaves.
Another theory has come to mind after reading chapter 36.5. Maybe, Inky isn't exactly changing the books into something the customer needs but is giving them supernatural perspectives. The translator note about the Ox in Ch. 36.5 says that it plays an important role in "To Live".
"A Painting is Worth a Thousand Words", I feel like Inky is using some sort of illusion/mental ability to Show the contents of the book instead of Reading the book.