I found A wrong right away.
Do you want me to put back this book on the shelf?
It should be:
Do you want me to put this book back on the shelf?
I just looked for the phrasal verb put back on this site, and it suggests that the verb is separable, with a question mark beside it. i clicked on the question mark and a new window came up, and in particular, about separable, it said:
Separable verbs With some separable verbs, the object must come between the verb and the particle: The quality of their work sets them apart from their rivals.
so this is a case where the object must come between the verb and particle. Otherwise it is wrong (and to me it also really sounds wrong, too).
Does this help?