Hi Pym,
the articles and strucures need to be set visible if you wish them to appear on the frontend. If you do not set it visible, the structure will not be shown in the navigation and the articles are not displayed.
If you create an article to inform a user that he filled in the email formula incorrectly you do this in a "hidden" structure because you don't want a stucture called "error" or "redirection" to appear in you navigation, don't you ?
The public stuff is for use with frontend users, so you can schow certain structures or articles only to logged users. These users are different from the backend users. But this feature (frontend login) is not yet done but it is on Olivers todo list, so be patient.
cu
Achim