For the Advanced Search option, there is a select box to choose a 'view' for displaying the results. This means you can specify which columns to display in your result set. You can do this by setting up a Custom Profile in the Admin section that displays the information you want. When you perform an advanced search, select the profile you want to view, click Search and the resulting table layout will be comprised of the custom profile information you setup.
1. create a profile and indicate it is used for search results
Note the fields have to be marked as "In Selector" to be displayed.
If you want to export this information, you will have to create a mapping in the export that corresponds to your custom profile.