Is it possible to only show a field on for example the 3rd level of categories? Now when I link a field to a top level categorie, the field is shown on all articles on all levels of categories, but is it possible to only show the for articles under for example a 3rd level category?
When you create your custom field. On the right side you can choose which category /categories this particular field will show in. In your case, from what I understand, you chose the 1st level category so if the 3rd level category is a child of the 1st level one it will show on the 3rd category as well. If you want to show on the 3rd level category only but with the same structure, you must choose the 3rd level category only.
There is another way to do it. If you flatten your categories hierarchy, you can choose any category and the custom field will show on the categories chosen.
One more thing... You must pay particular attention to access levels too. If your user is in a particular access level let say "Example A" and the custom field is in this access level "Example A" and the 3rd level category is in this access level "Example A" and the article is in the same access level "Example A", the user should only see this particular category and custom field. Quite a long and mind twisting answer but hopefully you get the point.
As a summary: Choose the most precise category "most deep in hierarchy" and choose the right access levels along the whole access level "chain" user->menu->category->article->custom_field