During checkout, I can add fields to billing or delivery information, but how can I add fields to customer information, or create another customized pane for them?
Example:
Student Information:
Name: Skill interest: Phone: Email: etc.....
You can achieve this using Ubercart Webform Integration module.
This module integrates two other modules: webform and ubercart. It allows you sell products directly from your webforms. It is particularly suited to be used as part of a registration system.
Using this module you can create additional field in check page.