Is there a way to associate a form submission with a specific user -- and then list all form submissions on the users profile page?
Is there a way to associate a form submission with a specific user -- and then list all form submissions on the users profile page?
No, currently users cannot see or edit their submissions without writing your own customization to do so.
Are there Gravity Forms functions that I can use (right now I am unable to see the documentation to figure this out)
No, there are no functions designed to be used on the front end to display entries. The only Gravity Forms function designed to be used on the front end is the gravityforms function that displays a form.
Gravity Forms is not designed to display and manage entries on the front end of your site, it's designed as admin functionality and accessible in the WordPress dashboard.
There are plenty of functions in Gravity Forms that are utilized, but they aren't documented because they aren't designed to be used outside the scope of the plugins internal operations.