Hi Jan,
The Custom Fields extension could certainly be used to add the product field. The DataTables extension will do live search of all fields, but there is currently nothing included to let you specify a search phrase ahead of time… plus, it will search all the fields that are displayed to try to find matching text. Each column is also sortable, though, so you could quickly sort the results by the “product” field.
Are you wanting it so that the visitor to the site chooses one of those three things to show the directory? Or, are you trying to set up pages that are already pre-filtered for each possible value of those criteria?
Either way, it sounds like you would need a bit of custom programming to do what you are wanting to do. Position and Location are actually stored as “categories” or taxonomies for the “member” custom post type, while everything else is saved as custom postmeta fields. So, the way you would search/filter for position & location are different than how you would do it for any custom fields you would add view the custom fields extension.
If you want to contact me privately, we can go over this in much more detail, and then I can give you an idea of what it might cost to custom program something for you.