Do I need to register a user account?

No. You can opt to not create an account. Doing so will mean that we cannot recover the data on your device if lost and that you cannot share data between devices. iOS users can access their data across devices using the same iCloud account without creating an account.

I am unable to find the "Upgrade to Premium" menu option.

If you have upgraded and have not created an account yet it has been replace with "Register Premium User". If you are an iOS user you can only Upgrade and Register one user per iTunes account due to Apple In-App purchase policies.