Hello everyone
I made the following changes and for now geometries are displayed correctly.
First of all I opened ArcGIS Portal and Insights in Internet Explorer instead of Chrome. Apparently Chrome checkes certificates more strictly and the certificate for Insights seems to cause problems. Even after exporting the certificate from IE and importing it to Chrome, it did not work.
Secondly I changed my basemap so that the whole world was shown and checked on the spatial reference of my dataset. Before that I had a basemap with only a small area in Europe and the spatial reference of my data and the basemap were not the same. So actually my data has always been drawn somewhere in the pacific ocean, but as my basemap only showed a small area in Europe I could not see it. I had a similar problem a while ago with another ArcGIS product, but I don't remember the details. So setting the spatial reference of input data and basemaps correctly seems to be critical.
Furthermore I have the impression, that working with services from a SDE-database is more stable and causes less problems than importing shapefiles or other data.
I hope, this helps.
Alena