Does writing a book improve your chance for getting scholarship for applying PhD abroad?
The goal of a PhD is to teach you how to do research. Teaching is not the primary goal of the PhD. Book publishing is also considered something that can be detrimental early on in one's career, since it takes time away from the other more important goals (advising students and postdocs, peer-reviewed publications, grants, teaching, committee work, etc.).

That said, a well-written published book probably can't hurt your chances. If, however, it's riddled with poor writing and technical errors, it will not help and may even do some harm.