For the navigation and getting it updated please explain a little more about what you would like it to be like. Currently if you login to the PowerCMS you should be taken directly to the index page with all of the navigation present.
As for the logout page it should be destroying the session and sending you to the login page. Here is the code that is at the top of the logout page:
This code should kill off the session then send you back to the index page. If you can confirm that your logout page has this code on it and you are not being logged out please let us know. There may be something else you can add to the page to ensure that the session is no longer available, if you add in an unset like this it should clear any values in the session:
You can put this just before the header call. Please post back and let us know the details.