Hi,
Sorry, I've been away for a little while and haven't been able to answer you on this. I truly appreciate your help, let's hope this issue can be resolved 
1) If I select the intermediary type Memberships, I get search results from the Memberships and not from Persons (which is what I need). If I query with Memberships how do I filter out the duplicate results?
2-4) Okay
5) Yep, I'm familiar with this.
Still the initial problem is this (copy-paste from above): When a user selects certain criteria, the search results may include multiple memberships even though showing one result (person) would obviously be enough. If I query with the intermediary type Memberships the same problem still applies. How should I change my view to able to show only one Person even though the search criteria applies for many Memberships?
I can provide you with a WP-admin link in a personal message if needed.
Thank you so much for your help,
Ilkka