Hi Danny,
Thank you very much for all the details, it helps us a lot!
1. I checked everything, but the configuration is okay. I tried to search a few queries for specific pages, and it worked, for example Det Sker Kalender.
2. I assume you mean the images on the results page. Unfortunately the plugin can not affect that. In the live results list, if the plugin finds an image, it will display it, but the results page elements are printed by the theme. There are theme API functions, which can be used in the theme loop – those will help fetching the same fields as in the live results list, including the image fetched by ajax search pro.