Alright, so for categories to appear I had to enable Sparkling categories plugin. Now I can choose the category, but slider is still broken on my home page - images are not shown, see screenshots above.
Alright, been battling with the slider for a while now. Figured out how to add ‘featured’ images to my posts. However, now these posts are appearing below the slider.
I guess I could leave it at that, at least for now.