re: How do I get ONLY the sub-category of a parent category to display on a specific page. Example: Display only the Bed & Breakfast businesses on their webpage in the STAY section.
Instead of making STAY, PLAY, DINE, SHOP, SERVICES root parent categories you should make Bed & Breakfast, Cottages, Campgrounds … and so on as root parent categories then you can use the enable_category_by_root_parent and category shortcode option to limit the display like you need. Does that make sense?
re: How can we differentiate between classes/types of businesses (Member / non-Member) AND affect how they are displayed (Icon / Colour).
The easiest way and the way I’ve used many times in the past in client work is to simply use CSS. If you look at the page source, each entry has it’s categories set as classes. So all you need to do is create a “Member” category assign your members to that category and then you can use CSS to do pretty much anything you want to highlight them.
Hope that helps!