Apologies, I missed answering this in a timely fashion.
re: When created are the listings on a sitemap and if not could they be or will they be in the future? I looked but it did not seem to be.
Presently there are not listed in a site map. This is on the to do list but I can not say when. With that said, I do not have any issues with Google crawling the entries.
re: Are the listings blog post or custom post types or neither?
No, they are not actually a cpt or a blog post. Connections is actually older than the cpt features in WordPress. I looked at converting it to use a cpt, but the db post schema is not the best suited for directories.
re: Is there a feed url?
No, there is no feed URL since it is not blog posts or a cpt.
re: Is Google Pinged with connections?
No, Google is not pinged.
re: Can it be monetized can I charge people to submit their own listings on connections?
No directly. Other users use plugins such a Restrict Content Pro to manage site memberships. Roles and capabilities can be used to define who can add and edit entries.
re: Does the plugin display wordpress seo settings or work with other seo plugins?
No, it will not show SEO plugins settings when adding an entry. Connections add its own SEO to its pages so it not required. This currently includes page meta title and description and page title. More will be included in future releases.
re Is it possible to have the listing appear randomly when people open the page?
Yes, see this doc page on the order_by shortcode option. Read the note about randomization for more details.
re: Are people who purchase entitled to lifetime updates or is there a fee?
No, updates are limited to an annual renewal fee. Renewing is optional. Any extensions will continue to function after the support license expires however, they maybe instance where an update will be required in order to keep functioning properly. I try to keep these types of changes to an absolute minimum by ensuring backward compatibility for as long as possible.
I hope this answers your questions thoroughly!