Is there a way to export the whole panelizer settings for a page? With whole settings I mean: context, layout and content. I know how you can export the layout and context, but I do not know how to export the content.

We have several websites that share some pages in common which have widgets in the panels and we try to automate that so that our content managers do not have to do this with every setup.
You can do this with Features:


Enable Strongarm module
Create new feature
Export and Deploy Panelizer settings


Alternatively you can do this with a custom module. See https://www.phase2technology.com/blog/exporting-panelizer-defaults-to-code/