Displaying a form for filtering in custom post type listing

How to build data structure into the Expert type, i.e. how to link an expert with attributes like “institution” and “research area”?

Answer
You may use Taxomonies in wordpress, to add extra level od categorization of your posts. In your example, you may register Institution and Research area taxonomies for your Experts custom post type.

With the above data structure built, how to include a filter for Expert listing as shown in the screenshot above?

Answer
You may use an ajax call to pass the filter criteria and receive related experts from the server.