Pilot on training flight reported a conflict with another aircraft that was landing on the same runway in the opposite direction of the traffic pattern.

Narrative

I was flying a Cessna 172S. I arrived at ZZZ airport in the morning at about XA:30AM local time. The runway in use was Runway XX. We were in ZZZ to do [student orientation flights]. I flew that plane from ZZZ1 airport. After landing I proceeded to do another flight for about an hour and came back to land; the runway was still XX and there were quite a few planes in the pattern for landing at ZZZ; I landed and proceeded to take my second [student] for her [flight]. After about an hour I was on my way back to ZZZ1 and the runway in use was still XX; my company airplane landed about 8 minutes in front of me; I made calls 15 miles out of the airport in the CTAF frequency then 10 miles out 5 miles out and on short final. Another planes that was doing pattern work at ZZZ was on left downwind for Runway XX and I was doing a straight in approach; that plane acknowledge that I was on final and that he would follow me to land as number 2.I proceeded to land and as soon as I landed and I was on the rollout slowing down and a Twin Piper Cheyenne had just landed on the opposite runway; Runway XY. I was already slowing down and I was able to almost come to a complete stop to see what this plane was going to do. He proceed to exit the runway immediately and I try to reach him on the CTAF frequency to ask him/her about the situation but there was no response. The aircraft never communicated on the CTAF frequency his intentions to land on Runway XY; also looking at the track data; he overflew the airport midfield and proceeded to make a right downwind for runway XZ; which I believe is the incorrect procedure as well to land on that runway. The Twin Piper never communicate his/her intentions and perhaps they were on the wrong CTAF frequency because when I tried to communicate with them there was no response. Nothing happened both planes were able to stop in time and exit the runways in a safe manner but the aircraft was on the wrong runway and never communicated on the CTAF frequency for ZZZ.