1) Can you please clarify what you mean by category image. Where would you like to use the image?
It would be used at the beginning of a post to denote its category.
2) I don’t think the space will be sufficient for a slider. You may use a smaller logo instead of big one. You can enable featured slider from the customizer if you would like to use a slider on your website.
So, I can just reduce the size of the logo and then enable a slider for the main page header?
Thanks!