Guust

Add this to your CSS:

.geodir_category_list_view li.gridview_onehalf {
    width: calc(50% - 5px);
}
.geodir_category_list_view li.gridview_onethird {
    width: calc(33.3% - 5px);
}

This should help too to see how to change the 4 and 5 grid:
https://wpgeodirectory.com/docs/customizing-your-style/

You also need to delete the next

}

Cannot really help with that. Did you consider the CPT Categories widget? That will link all categories and child categories.
https://wpgeodirectory.com/docs/widgets/#cpt-cats

1. There was a missing space in the CSS code, fixed in your site and my post above.

3. I think we need to get the developers to have a look at this. The fields should indeed not be there.

You can change the templates that come with GDF for the non-GD pages, just remove the sidebar.
I have no idea about Divi builder so cannot comment on that, maybe the developers of that plugin can help?
Here is some CSS help: https://wpgeodirectory.com/docs/customizing-your-style/

I have now added the map widget to the GD Home Top section, the way it is normally done. Delete one of the maps to make it work again. The map shortcode in the header does not display the listings.
Our sample pages use a GeoDirectory Framework child theme. Because you use a different theme, the theme template would need a re-design to achieve the full width map on Listings and Location pages.

Because your pages setup, your location swithcher does not work, for example, it takes you to /partner/directory/oesterreich/ which does not exist, but /directory/oesterreich/ is the correct address. You need to remove the GD pages from under the partner page.
If you want to rename Places in the URL, you do that at GD > Permalinks > Listing url prefix

If you disable physical locations, they cannot show on the map, that is how it works. You just turned the map off for your main CPT it seems.
You would normally do that only for a CPT for which you do not want addresses and no map display, like worldwide freelancers.
I still do not understand what you are trying to achieve. Why do you want different sites to display different listings? Why not display all listings on the same site?