Will I be able to edit or delete my payments before I submit them to the Department of Revenue

Yes. TNTAP gives you a view of all pending payments.
To find pending payments:
1. On the home page, in the “I Want To” section, select “Manage Payments.”
2. Select “Make Payments and File Returns.”
3. In the “Show” section, select “Payments" from the first drop down box and "Pending” from the second drop down box. 
4. In the status section, select “Delete” and confirm by clicking “Yes.”
Now, your payment has been deleted.