A pilot reported a NMAC while practicing ground reference maneuvers in the traffic pattern of a non-towered private airport.

Narrative

Inadvertently practiced ground reference maneuvers near a private airport and plane coming in for landing flew above me coming in on their downwind in the traffic pattern. While entering the downwind; pilot asked traffic in the area if are on radios and I responded. Pilot mentioned I am flying near the private airport and his position and that they are flying above me on downwind. I found traffic and noticed separation and noticed the proximity to the airport I had moved into and quickly departed the area and mention my intentions on CTAF. As I was leaving; I heard the pilot that was in the pattern mention that there are two other aircraft in the area practicing ground reference maneuvers in close proximity to the private airport while they were on downwind (very busy training practice area).Possible error on transponder as well. On the way to ZZZ; tower mentioned for me to squawk VFR which made me think if the transponder was working or off prior to the call. Made my before takeoff checklist; so unsure what it might have been. After squawking VFR; I asked tower if that works and they confirmed transponder is working.