Hi Andrea ,
1) I am not sure how the directory plugin ( which one is it ?) that you are using works but with some costum coding you can probably Make it work. You will need to find the right hook that being execute before or right after the form submission ( of the profile/listing) and use it in order to get the address the user entered. The address you will need to geocode and save in the GEO my WP table in the database. GEO my Wp comes with a function that will geocode and save the needed data. I can post the name of the function later when I'll be on my computer.
2) I would assume that plugins will usually use the featured image to upload and save images to a listing. But if that is not the case with the plugin you are using you will need to find how/where the image is being saved in order to display it. Then you can open the results page that you are using in your search form which you can find in:
Wp-content/plugins/geo-my-wp/plugins/posts/search-results/ name of the search results you are using/results.php. In that file and you wills see the results loop which you can edit and display the image.
Let me know if it help.