I Agree. The phrases "I also have a book" or "I have a book too" sound ok, but "I too have a book" does not sound correct.
This translation is formal/literary; "I have a book too” is what we would say in conversation and is correct.
From what I understand, "I too have a book" is the more accurate answer. In English, "I have a book too" is ambiguous - it can mean "I have a book (as well as other things)" or "I (as well as other people) have a book". The given sentence has only the second of these meanings. To convey the first meaning, the "bhi" would need to be placed after "kitab".
If it was "I also have a book" then that would give the correct meaning and be an acceptable translation, but "too" is usually put at the end of a clause in English.
When using words that indicate position (पास, सामने, पीछे, आगे, etc.) the possessive pronoun becomes oblique (because these words are modifying the subject). मेरा/मेरी is only for when they literally translate as 'my'.
I too have a book is not grammatically correct in English.The correct form is I have a book too or I also have a book.
It is not correct in English.I wrote it in the wrong way only to be accepted by Duolingo.