1: No
2: imperceptibly, but yes, it does change
I understand your argument that the earth referenced kinetic energy of the aircraft will change as it circles in an airmass that is moving in that same frame of reference. However, I don't yet accept that this change in kinetic energy influences the airspeed.
The aircraft is assumed to be circling in a completely uniform volume of air. Suppose we place a gas balloon in that same volume of air and it carries an observer. The aircraft circles the balloon. The motion of the aircraft and its knetic energy can be referenced to the observer. (The frame of reference for kinetic energy can be whatever we define it to be. It does not have to be earth referenced). The observer will see the aircraft circling with constant angular velocity and constant altitude. In the observer's frame of reference the aircraft energy does not change. There is no reason for the aircraft indicated airspeed to change.
Why would the presence of the balloon and its observer change the way indicated airspeed behaves?