Hello @ahejlik,
The header image you set in Onefold theme is designed to be displayed in the blog listing page header and individual pages. Please check if the image is displayed in the header of your individual pages.
For the slider display issue please make sure that under Dashboard > Appearance > Customize > Featured Slider Slider Type > Enable Slider on > static front page is Selected and featured pages are set.
If the above steps does not help you resolve the issues, please share with us your website URL so that we can inspect your website and further debug the issues.
Hope this helps you,
Best regards !!