Why anonymous users can only see 1 link in navigation menu? I'm trying to show navigation links to anonymous users/ visitors of my site. However, they can only see 1 of the many links while the administrator can see all links just fine.

I'm using Drupal 7 and Zen theme.

My settings : http://i.imgur.com/MVRwejG.png

This is what anonymous users/ visitors see: http://i.imgur.com/3uNNR9Y.png
That is because they do not have the necessary permission. So for example they do not have permission to create contents of type (article, blog, basic page and product) in your case. And I want to believe you don't want anonymous users to create products, pages, e.t.c.

To assign anonymous users new permissions, go to admin/people/permissions