Steven Zahm@ Damon
The [connections_form] shortcode has been deprecated and is no longer supported which is why you will not find any documentation about it other than mentions in older forum posts. The reason is it is not longer needed at all.
I see you purchase the Extension Pro Pack. You have everything you need to set it up so Form can be used to edit entries on the front end.
Go to the Connections : Settings admin page and click the Display tab.
In the Results List Action section enable the “View My Directory Entry” or “Add My Directory Entry” option. Leave the “Submit New Entry” disabled unless you still want to permit anonymous submissions. However, that could end up being very confusing to you and your users. So I suggest not.
In the Entry Actions section, enable the “Edit Entry” option.
No go to the Connections : Roles admin page and give the users roles that you wish to moderate the Add Entry Moderated and Edit Entry Moderated capabilities.
Lastly go to the Connections : Settings admin page and click the Form tab. Configured as desired. This settings page replaced the shortcode which is why it is not needed any more.
Hope that helps!