Is there any way for apps to access your iTunes email address, in order to use this as a unique identifier to identify a specific user? I'm trying to figure out how certain apps can uniquely identify users outside of IP, Device Name, and Advertising Identifier. Is this a possible way?
No. Apple doesn't provide an API to developers to allow them to access your Apple ID.
The only way a developer/app can get your Apple ID is if you explicitly give it to them and they store the contents.
One way an app can uniquely identify you, other than you've already indicated, is by storing your IMEI number on their servers. We just saw this happen with Uber.