I was wondering if there is a way (using some hooks for example) so the child pages in a book respect their parents access level, meaning if user doesn't have the access to view the parent node, he won't be able to view the child nodes as well?
I use Drupal 6
I had a similar issue where I wanted the book main page's author (aka owner) to be able to edit all the lower level book page's even if they did not create the pages.
My solution was to create a custom module called 'Book author access' (http://drupal.org/sandbox/jrockowitz/1396474), which use the 'ACL' module (http://drupal.org/project/acl) to control a book's pages access levels.
The 'Book author access' module does propagate the view, update, and delete permissions of the main book page to all to lower level pages, so it is possible that if you use the 'Content Access' module (http://drupal.org/project/content_access) and limited the view access to the book's main page it would solve your problem.
If you are not a developer then my answer might not be that useful...sorry.
As noted in my comment, I think the Book access module probably better addresses your requirements, just look at the below screenshot.
