In both "normal" and "slow" the last sound is clearly 'И' ('книгИ'), but this answer is rejected (Duo expects 'книге').
Both answers are grammatically correct in Russian - the first one (ends with 'книги') answers the question 'Where should we write to?' (to our books), the second one (ends with 'книге') answers the question 'Where should we write?' (in our books), but given that the audio clearly sounds 'книгИ', I reported it.
No it does not, на means that в книге in the book в книгу into the book на книге on the book на книгу onto the book
What is the difference between пиши and пишите?