Fixed now. Two things had to be done:
Configuring the top navigation menu. To make Calendar and / or Agenda show, you also had to include these options into the “top menu” setting, as that setting was locally overridden in your site’s configuration. Now done. That menu can only include a limited number of items, so I removed “Bookmarks” in order to include the other options. That at least started to show the Calendar and Agenda menu items on the “All Categories” page.
Re-configuring category settings. The per-category setting to show the Calendar and Agenda menu items is overriding the global setting, and there seems to be a bug in there. The menu items were only added after I unchecked the per-category event plugin settings, saved, re-checked them, saved again.
Events are added as topics with a special additional field in them. So just start creating a new topic, and in the editor that will show up (1) first select a category if not already done, (2) click the “Add Event” button around the top of the editor window, (3) add title and description and save it. It will now show up in the calendar and agenda views of its category and in the global calendar and agenda that is shown on the frontpage. I just tried it with a test event, that I have deleted again now.