Please post a link to an article containing an example popup.

Since updating JCE Editor to 2.9.57 the MediaBox Popups show not only the content of linked articles but also all menus and modules of the page.
Updating to version 2.9.58 didn´t solve the problem.

How to show only headline and content of articles in the popup as it has been before the updates?

In order to prevent the display of modules and other full page elements in the Mediabox content, MediaBox adds &tmpl=component to the end of the content url when it requests the data, which should make the template render the content without menus and modules.

MediaBox is doing this correctly, but your template is not, and is still adding the modules, so this has nothing to do with the recent JCE Pro or JCE Mediabox updates.

Here is an example of a URL that MediaBox has altered, but that is still rendering the menus (first item - Martin Adendorf) :

https://aai-aachen-koeln.de/index.php/infos-fuer-studierende/dozentenverzeichnis?view=article&id=139:martin-adendorf&catid=17:dozenten&tmpl=component