Hi!
Unfortunately I cannot accept customization requests.
If you update the plugin to the latest version (4.7) it will allow you to change the layout of the category/term selectors to radio buttons: http://i.imgur.com/xJ6ZpnC.png
That should solve one of your layout requests. If the “affiliation” and “lesson types” are taxonomies, you can select to display them on the Frontend Search settings -> Taxonomy Terms panel.
The layout of the category and taxonomy selectors is printend in this file: wp-content\plugins\ajax-search-pro\includes\views\asp.shortcode.categories_terms.php
However I do not recommend changing it too much, it will affect the search process as well, be very careful.