I'm creating a site on Drupal 7. There are fields 'sitename' and 'site slogan' in theme settings but I need at least two more fields to show some information in header. How can I do that? (I'd like to keep Bartik, I know that choosing another theme is some kind of solution)
Maybe you should just add some custom blocks in that region? (Structure>blocks>add new block)
If you think that you are going to customize a lot the Bartik theme, I'd suggest you to create a Bartik's subtheme to customize the default Bartik. To do so, please follow the guide: https://www.drupal.org/node/1114190