2.
I also realized that the feature image of the blog page itsself is not pulled. The blog page uses the same hero image header element like in posts. http://dev-1.upconversion.de/test-2#more-1650
3.
How can I achieve a margin to the left and right in mobile /tablet mode for the blog archive page?
Regarding the first issue:
I unchecked the display padding around images option and it looks perfectly aligned in mobile view, but not in tablet and desktop view – here the the image is overlapping somehow.
Unchecking the Display Padding option removes the padding you have set in Customizer > Layout > Container > Padding – change this to 30px to match the CSS you have added….