on the mysite there is a section with the documents which I'm following. Is there a chance to display these documents in a Webpart on another site?
Thanks in advance!
The Docs I am following WebPart is just a ListView on the "Social" list present in the My Site. So you will not be able to put the WebPart in any other site.
However, you can create your own custom webpart by using the REST API:
http://<site>/_api/social.following/my/Followed(types=2)
This will return the documents followed by the current user. You can call this REST query from JavaScript residing in a ScriptEditor or a ContentEditor WebPart.