Flight Instructor reported a NMAC with another aircraft that was flying in the traffic pattern for an intersecting runway when the opposite runway was in use.

Narrative

Aircraft Y caused multiple conflicts with several aircraft and two near-misses with my aircraft when said Aircraft Y was operating on a crossing runway that was not the runway in use by all other aircraft.The first near-miss occurred on final approach at approximately 150 feet above the ground. The subject aircraft was on final for Runway XY while I was on final for Runway XX. The subject aircraft said he had me in sight; so I made the incorrect assumption there was no risk of collision; and returned my focus to the runway ahead because another aircraft was just clearing the runway ahead of me. A few moments later I got him in sight as he pulled up to fly over the top of me. I estimate the separation was 300 feet laterally and 100 feet vertically.The second near-miss occurred when I was on downwind for Runway XX. The same pilot in the same aircraft departed Runway XY and climbed straight out toward the downwind leg of XX. I did not have the aircraft in sight; but I got an aural traffic warning from my avionics system and was able to spot the aircraft in time to pull up to avoid a collision. The other aircraft also took evasive action. After the second near-miss with the subject aircraft I chose to depart the area immediately.The pilot of Aircraft Y was chastised on the radio by other pilots but claimed that the wind favored the runway he was using. At the time of the event there were 4 aircraft using Runway XX; and one aircraft (the subject aircraft) using Runway XY. Winds were reported at 300 degrees at 4 knots. While the pilot of Aircraft Y has a valid point; the winds were not strong and Runway XX is the primary/designated calm wind runway at ZZZ. I believe that the pilot of Aircraft Y exhibited a hazardous attitude when choosing to operating on a crossing runway at a busy airport when all other aircraft were using a different runway.I believe I also exhibited a weak sense of judgment by continuing to operate in proximity to this aircraft. I should have given this aircraft a wide berth after observing their disinterest in participating in the normal flow of traffic in the pattern. If I had left the area sooner the second near-miss could have been avoided entirely.I note that ZZZ [Airport] has a reputation for this kind of behavior in the local community. I believe the FAA or the Airport Manager should take action to reduce this kind of behavior and improve safety.