I will sum the logic through 4 easy questions:
- Can/should private pages have public child pages? (it seems private pages are using other site or context for any group/user)
- Can/should public pages have private child pages?
- Can/should hidden pages have non-hidden child pages?
- Can/should a page which certain user is not allowed to VIEW have a child page which certain user is allowed to see?
Does some of the previous scenarios change parent page’s behavior? I mean maybe allowing you rights to a child page makes you automatically authorized to see parent page.
Furthermore, what is the difference between hidden and *non-hidde*n pages? I can browse both through links!
In answer to your questions (for Liferay 6.1, may differ for earlier versions):
be hidden (so they don’t appear in the navigation but can be
accessed directly by the URL)
you’ve changed your theme so that they do
theme to have that restriction or not
Parent page behaviour is not affected by child page settings.
Hidden page: Pages that are hidden from the navigation but can be accessed directly via links or typing in their URL
Non-Hidden pages: Can be seen in the navigation, and can accessed in the same way as hidden pages.
Private pages: Can only be accessed by authenticated members of the community that they belong to. They are effectively gated pages so hidden from public viewing without having to set the page permissions for Guest users.
I hope this answers all your questions.
~~ EDIT ~~
As Julien Lafont as mentioned below: Hidden pages are visible in the search portlet. If you want to hide them from a particular group of users, use permissions. Thanks Julien.