page with categories on it

Hello,

my question is how to make a page and add the categories menu to it, here is the site where i want to include this feature:

http://islandofopenprocess.net/?page_id=64

so under the picture and short text there should appear this menu

http://islandofopenprocess.net/?cat=3

is it possible to combine the two features? I would also like that the circle where it says category / atb would be not anymore on the site.

I have child theme and custom css installed

Thanks in advance

Best

Martin