Hi,
Yes, Events Manager creates separate pages for each category.
I realized that I can access these pages from the “categories page”, but how can I add these pages to the menu?
By the way: When I asked this question, the single category pages did not work because there is a bug with WPML and Events manager. I disabled WPML and now it works.
You should be able to do this via Appearance > Menus.
Oh, I see that I can add the category pages there, you are right 🙂
But when I open a category page, the menu entry will not be highlighted (has not the current-menu-item class). How can I add the highlighting for the category page and the events from this category?
I think that is more of a theme/css issue, you can ask your theme provider about that and they may have quick fix or snippet about this.