The search bar possibly isn’t there when you are a guest. I remember trying to decided whether to allow guests access to it or not and I guess my decision was not. I’ll add back later on today if I have time/remember.
You can remove a page from your list of pages, but you can’t add it back in at another point on your menu without using the custom code option.
If you leave your menu the way it is now, but add the "Custom Code" option as the last menu item, and use the code I posted above, a "Contact" page should appear at the end of your menu.
Hopefully that makes sense ” title=”Smiley” />