For the first list I think you're just looking for a regex that does NOT match the category you want to exclude. I haven't tested this, but try the regular expression
^(?!13$)
So you would end up with:
{exp:stash:get_list name="articles" match="#^(?!13$)#" against="category_id"}
...
to see if that finds all items in your articles list that are not category 13. (Updated, changed regex after test run.)