How to add Log Out or other profile menu elements?
For BuddyPress plugin you can create profile menu.
Create new menu and choose from BuddyPress section what pages to show in that menu
As this feature comes from BuddyPress you can read more about the plugin here.
Why I can’t see all menu items in left Menu Bar?
You need to make sure that all the Menu items activated from Screen Options
From Dashboard=>Appearance=>Menus click on the “Screen Options” button on top right corner and make sure all check-boxes are marked.
In this way you can add icons or labels to Menu and have in Menu categories, posts, pages, reactions, ranking and other taxonomies.