Is there a way to add fields that can only be filled by Administrator of the account after the application has been received?

There are a few questions that I want to add to the top of the form that are only visible to me as the administrator when I print responses. This would be for me to indicate whether the application was approved or not. 

Yes it is possible to achieve your requirement by adding "Hidden Box" widget in form. This field will not be visible to user but when you as form owner edit submission, this field will be visible to you. 

You may like to take a look at the following guide which should help you: https://www.jotform.com/help/194-How-To-Assign-Status-To-Submissions 

Hope this helps.

Do get back to us if you have any questions.