C172 pilot reported malfunctioning transponder and ADS-B readout increased conflict potential resulted in a NMAC situation.

Narrative

I was the left seat pilot in Aircraft X flying with a safety pilot. Approx. five minutes prior to the near miss; we were informed by ZZZ Approach that our transponder was reading an error and to re-squawk. My safety pilot typed our assigned transponder code back into the transponder but ZZZ Approach advised us that we were not reporting ADSB out regarding our altitude. A few minutes go by and then my safety pilot advises me of possible traffic off of our right nose; inbound 600 ft ABOVE us but we are on a collision course. I immediately start our decent down a few hundred feet to establish a safe 1000 ft distance between us and the traffic. However; during our decent the safety pilot is not able to obtain visual of the traffic and we receive a traffic alert from our avionics. He tells me to take off my instrument simulation glasses because traffic is not insight and we are right on top of each other. I take off my glasses and within seconds of scanning for traffic I see the SR20. The SR20 is flying less than 200 FT under us. I observe the aircraft fly directly under us from the front right side of the aircraft. I loose visual when they are under us but quickly reestablish contact as they fly out from under the left side of our aircraft. Aircraft Y flies away and we continue our direct navigation to our destination of ZZZ1.Here are the multiple smaller failures that lead to this near miss. XPDR (Transponder) failure on Aircraft X - This did not allow Aircraft Y to see our ADSB out regarding altitude.No traffic alert was issued from ZZZ Approach despite being on flight following with them.Aircraft Y appeared to have 'dove' under us. However this is only a conclusion drawn from the the ADSB-IN data we were receiving that indicated they were at +600 ft above us when we first notices the potential collision; and then at the time of the near miss they were now lower than us despite our efforts to decent. From the information available in the cockpit it was determined that Aircraft Y dove under us. This could also be the result of a inaccurate ADSB-IN reading onboard our aircraft that falsely indicated their position as higher than ours. Aircraft X did not take any horizontal traffic avoidance. Opting for only vertical avoidance maneuvers allowed both planes to continue on a horizontal collision course despite the intended 1000 ft of vertical separation. Safety pilot of Aircraft X should have prescribed a 'Right 360' or similar evasive maneuver to separate aircraft much sooner than what was executed. Both aircraft should have executed horizontal and vertical maneuvers in order to eliminate any possibility of collision.