Apparently it was possible to export a web part and import it on a different site with SP2010. This does not work anymore for SP2013. I also tried to edit the *.aspx directly, but it always throws me the following error:
List does not exist. The page you selected contains a list that does not exist. It may have been deleted by another user.
The content search web part is able to display data from another site, but can not be utilized like a list web part.
Is there any possibility to insert a list web part on a different site without losing its functionality?