How do I remove or disable the Search Courses form on the 'All Courses' page?
Or
How do I get it to work properly? Does it search by course name or category?
http://www.coop-solutions.ca
If you go to 'All Courses' and search 'family mediation', there should be 2-3 courses out of the 11 listed that should come up in results, but it doesn't do that.
If you want to remove the search form from course directory, then use this custom css:
.directory.course .dir-search {display:none;}
I checked your site and the search form was working fine, when you search 'family mediation' then it shows all the courses because every course has mediation term, try to search with a unique word then you can find your course.
Also if you want to search from category, paid, free courses, then use different directory layout and in sidebar you can use widgets for filtering the results. Also enable the course category/level/location redirect setting from wplms->course manager, to show it on course directory page only.