What can be done to make Membership - Membership Status in particular - a Result Column for profile searches? I want to be able to show Status in a Search View.
Can't you go to Advanced Search & select the memberships you want - you can select which statuses you want, too - the results show status and date of membership if you select to Display Results As Membership - unless I don't understand your question.
Note: For v4.5 and below, Display Results As is in the top right of the Basic Criteria frame in an Advanced Search.
In 4.6 Display Results As is in the "Search Settings" grouping at the bottom of the Basic Criteria frame in an Advanced Search.
With regard to finding people who have aren't members, if you can't do this via a view I think you will need a smart group of people in your Group who have a membership and then use the include/exclude custom search (or perhaps Search Builder) to find people in the Group but not in the smart group.