Is there a way to allow a completed form applicant receive a confidential list of all other submissions?

I want all the form data to be available to just the people that completed and submitted their application. 

Yes. You can generate a report of submissions and redirect the user to see that report after submitting the form. You can create an HTML table report by following the guide How-to-create-an-HTML-Table-Listing-Report. You can also have password protection to access this report to keep it secured.

You may redirect to the report URL directly using Custom URL or can have this report embedded on Thank you page message. 

Please see the following form to see how this works.

http://form.jotformpro.com/form/42674760781968?

Please get back to us if you need any further assistance. We will be happy to assist you.