You have actually started a THIRD topic here, which makes it hard to follow and respond to any of them. If you have additional questions, please start a new question for them instead of asking new, not related questions in the original thread.
1. Page on the Menu
You did not confirm if I understood your question correctly – are you trying to add a menu item that will allow a logged in user to go to the Pages editor?
That is NOT really a theme related question – but rather a more general WordPress question, which is why I merely suggested a couple of approaches. We are not here to totally hold your hand on non-theme issues, but will try to steer you in the right direction. Bottom line, if this is want you to do, opening the Page editor is simply providing a proper link for the user to click at some useful location – perhaps as a custom menu item with a custom link. If you just include that link on a custom menu item, then non-logged-in users will get a login page instead of the page editor if they click it. That is a really the simplest way to do it – but you have to know how to use the WordPress custom menu editor – that is not a theme issue.
2. Page with Posts
Page with Posts allows you to display any post type with a bunch of filtering options. It is not an implementation of Custom Post Types, although you can display Custom Post Types if you know their slug name. It is most commonly used as a way to manage your post content. At the simplest, one can serve as an alternative to the default WordPress blog page that allows you to use all the Weaver Xtreme per post and per page display options.