Objects origin is not moving in edit mode I probably messed up some of the settings but I couldn't figure it out my selfe.
The problem is, that when I move the wohle mesh in edit mode the objects origin isn't moving with the object, but the pivot point is nevertheless still in the objects center.
And the reason I think the problem lies in the blender overall settings is because I started a new project and tried the same thing with the default cube. The problem is still the same.
Pivot Point and Object Origin are different things.  The Object Origin isn't meant to move in edit mode.  The Pivot point depends on the Transform Pivot Point setting.  Take a look at the top bar in the 3D window: 
The second drop down sets the pivot point: 
You haven't screwed up any settings.  You just have the Pivot Point set to &quot;median point&quot;. Because you have selected a cube, the median point happens to be the center of the cube.
If you want to pivot along the object origin, change the drop down to &quot;Individual origins&quot;.
To move the origin, in object mode, Right Click and select &quot;Set Origin&quot; from the popup menu