Is the pronunciation of "gi" as "yi" deliberate?
Yup. It's supposed to sound like "yi."
This would imply that its someone elses book, not his? And if it was his book it would be; Kan du gi meg boken til meg?. Idk sorry
I think what you wrote is "Can you give me the book to me?"
"Kan du gi boka mi til meg" would mean "can you give me my book".
However, "can you give me the book" doesn't imply anything about the book's owner, imo.
Can this be used as "can you hand me the book?"