If you are not moving the stick, but have your hands off of it, and the graph is moving around, you may need to have the stick pot replaced. That movement could indicate a dirty stick pot.
Is it possible that I set up another model in the Tx in a "GROUP" setting that has now made the above condition standard for all my models?
One model setup cannot affect another model setup. They are completely-different. Settings made in one model will not affect the settings made in another model. If that is, indeed, happening, then there's something seriously wrong with your transmitter, and it would need to come into the service center for repair.
I am using a default/new model slot with default settings setup as a heli. I also noticed that if I run the throttle stick all the way to the top against the stop and I move the stick full left and full right but against the stop the entire time, I notice the vertical line moves either decreasing or increasing in value by about 15 points. I would think this value could not increase or decrease since the stick is at the full top position against the stop?
When you hold the throttle stick at full deflection and then move the tail rotor function, the throttle should not change. That indicates you likely have a dirty stick pot or possibly a damaged stick assembly. Again, something for the service center to examine.