@ Pieter Hartsook
1) Connections does support many custom ordering options, but only set at the shortcode, it is not user select-able. Here’s the link to the doc page. One of the options are a random order, so that may suit your needs.
2) You could create an image map so it links to a specific sets of search results within Connections, but you would have to create the image map, Connections doesn’t have that built-in.