Hi!
1. You can change the results box width here.
2. By default, taxonomies does not have images in wordpress. If the taxonomy images are stored in a custom field (term metadata), then you can enter the field name here. It is a very common method.
If a different method is used for the image storage, then probably a custom code will be required to fetch the images and fill them in to the results list. Usually the plugin/theme developer (which adds the taxonomy) knows how to get them by their ID.
I tried to log-in to check if I can tell by looking, but I was not able to access the wp-admin section, and the log-in via clicking on the login icon did not work with the credentials.