User rights: Only create, edit and publish articles There is a user role where users can edit, save and publish articles. But they don't see the admin menu. 

Does exist a module to realize a "create content" button only or to modify the admin menu?
There is no specific module for that, and it is well known problem. But if you want them to only create one content type, like Article, you don't need a module for that. You can simply go to /admin/structure/menu and add links like /node/add/page to a menu they can access.

For node listings for such users, create a view with table of titles and edit links.