For example on a person's profile page the profile picture and the cover are visible to everyone even the unregistered. How can I change it? and in the search pages?
In the studio, go to page management, find the desired page, edit the blocks. Now you can control who sees certain blocks.
I understand it but I can't find where it is to change the visibility of this particular page.
Search page will be added to page builder in UNA 12, so you will be able to hide search page for guests then.
Not logged in users can't 'Comments Post'.