Ok, now I understand... Forget about Collapsing Categories...
You can make separated Custom Menus at Appearance -> Menu. Make a menu named, let's say "Bodypart". Add "bodypart" category to it, but say as Navigation Label "All"... Now add the subcategories. By drag and drop you can arrange the order. Save the menu but don't assign it to any navigation bar. Don forget to save, the menu isn't created without save.
Now go to Appearance -> Widget and drag the Custom Menu widget in sidebar. In the widget box, set the name of menu to "bodypart". Do the same steps with all categories... In that way you will have categories organised like on "exercises" site, except only that yours will be in one column, not in two.
For an advanced search, with filtering by more fields, you can use: http://wordpress.org/extend/plugins/wp- ... ds-search/