Why do we use ved here?
Unfortunately, I can't give you an explanation in grammatical terms, but 'ved' is optional in this case. "Katten sad og rørte maden" is also fine
There is this post that a user has made, we also have an overview of grammatical discussions which you will hopefully be built upon, too
You must use your danish mindset to comprehend it.
at røre mad har mad has 2 translations "to touch" or to stir" in this case" stir "is appropriate