I just activated the plugin and it works for me. I got the results in under a second, which is extremely good: https://i.imgur.com/TUGiRGf.png
I could not test this on mobile, because the widget area does not show up there, so I can't tell if it works or not on my devices. Try to put the search elswhere, maybe the theme has widget positions for mobile screen sizes. Your theme is responsive and it hides the sidebar on mobile screen width, which contains the search.
The geolocation search depends on how the geo data is stored for each post. If it's a custom field, then it should be all right. All you will need to do is to select the custom field which contains the gelocation data. Here is a quick info about custom fields from the documentation: http://wp-dreams.com/demo/wp-ajax-search-pro3/docs/#general_options_search_in_custom_fieldsBest,
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