Guust

You can export your data with the CSV export. That would give you all the data you want.
Anything else would be a customization.

It looks like I guessed right.
I have turned off automatic geolocation, so now it does not seem to happen anymore.
What was happening is that your visitors’ location is detected on second load, and listings/category pages will always adjust to the location set by the visitor or the browser. Therefore on the second load, there are no relevant listings.
You will have to delete your geo cookies to see the change: https://wpgeodirectory.com/docs/faqs/how-can-i-clear-geo-location-settings/

I don’t think there are any other icons for that than those shipped with the plugin.
But let’s ask the others too.

Documentation can be found here:
https://wpgeodirectory.com/docs/category/addons/

I suggest you have Places, and then have categories like stay and dining.
These would be your category pages:
http://www.chattersolutions.com/places/hotel-1-1/
http://www.chattersolutions.com/places/bandb-3/

https://wpgeodirectory.com/docs/places-categories-and-listings/

Or do you mean in the ribbon on the bottom of the home/location map?
I see all CPTs listed there.

I have set it to 1068 wide since that is your theme size, at
GD > design > scripts > css

This is the code I added:

#geodir-wrapper {
    width: 1080px;
    margin: auto;
}

Please check, thanks.