fixed turns about a point are one of the required demonstrations to get a commercial fixed wing license, which describes a circular pattern on the ground.
not sure a transponder setting has anything to do with the aircraft type, but 800' @ 80kts sounds about right fir a small single engine. why over metro, other than orbit surveillance dunno. training was always done out in the country, away from populated areas because you did get pretty low. iirc, the formula for entry altitude was 10x airspeed. and altitude varied depending on the wind speed and direction.