Hello Vlad,
I've checked your modules:
Category - You have specified only to show category id 1:
http://screencast.com/t/lEryb5ydOR and this category is unpublished:
http://screencast.com/t/OzJtj7DsmBBE . That is the reason why it did not displayed.
List - You have enter private category here:
http://screencast.com/t/6AwIXXyShr . Can you show me where did you put this module so I can have a look.
Related - This module will be displayed if you viewing the blog entry only. This is because Easyblog want to get the blog data to search for any related blog by tags.