How To Develop a Mobile Interactive Book Application/Game ?

Xcode with objective C#. The game engine on the other hand I wouldn't have a clue; to me I'd say you'd have to make it yourself.

What engine can you suggest to create a similar one?

None of the major game engines are a perfect fit for a storybook. An experienced group would just use whatever tools they were most comfortable with. For an inexperienced developer I'd suggest getting some experience first.