It explains how to display categories on category page, to display on home page select “Pages” tab from right top of screen instead of “Sidebars”. By default there “Categories” widget on home page with “Fixed 2 levels” display mode, change that to “Fixed 1 level” display mode.
Regarding icons for each category we do not have that feature in Classibase.
By the way I like your website design, it looks professional and unique.
One more thing: we noticed that you modified base theme and not changed /base/ folder. To be safe and stay not effected by theme updates please rename folder to something unique for example to /snejk-base/. Then re-activate theme from admin panel “Appearance”->”Themes” page.