navigation.php behavior / switching off

Hi!
navigation.php (template-parts/navigation.php), which is supposed to give you the browsing capability through the posts (when single post is displayed) does so with very limited usability. It browses through ALL the posts, regardless of tags and categories. This becomes not only useless, but embarassing quite soon.
My question is two part:
– how to correctly turn that feature off – erasing all code from the file did the job, but I would kind of more like to do it properly (eg, disabling the call for this file altogether).
– is it possible to configure this feature to browse only through a certain category? This way it would be nicely useful. Or is some other function / widget used for this?

The linked webpage is a mess, just used for testing /demonstration purposees.

I realize this is a newbie question, but will appreciate your help much!

The page I need help with: [log in to see the link]