Hi Scott,
1. Competencies cannot be linked directly to a task, activity or resource. They can be linked at the course-level.
2. I had a look and couldn't think of a way to make the competencies with their linked courses searchable. You can setup the role permissions to allow a user to view the competency hierarchies, so they could go in and see the course linking, but it's not searchable. I think your best bet in this case would be a custom report source, as the data is there it's just not being presented.
Thanks Scott!