re: When we update Connections in the future, will we need to re-edit that widget each time?
No, only when the Widget Pack is updated.
re: We’ve made so many tweaks here and there, I have to keep track so we don’t suddenly break the functionality with a simple update.
A quick scan over topics/replies it appears the only changes were shortcode options (sorting by the meta key/value) and a minor CSS tweak added to a custom CSS plugin for the Gridder template. So far seems like updates should be pretty safe to do unless I missed something a bit more critical than that.