What Tasker tasks require root access?
The simple answer is that it requires root to do things that would require root if they weren't automated by Tasker and you were doing them manually.  Tasker is irrelevant.

Edit: Turning on/off GPS does not require root.  Apps must be able to do it, because Power Widget can.  As for the lock screen, I think what you read must have actually referred to the keyguard (the "swype to unlock" screen).  The phone is not locked the same way as it is with a pattern/password when the keyguard is on; it's just to prevent accidentally keypresses, not for security.  Tasker can disable the keyguard.