Low wing Pilot reported a high wing aircraft pilot making inaccurate position reports; landed opposite direction; resulting in a runway incursion and severe ground conflict.

Narrative

I was with another pilot in the Aircraft X. We had been in the airspace for roughly 2.5 hours. I made a 12 mile final radio call for Runway XX. A minute or so later; the Aircraft Y tries to contact Tower; which is; and always has been closed on weekends. I respond and tell them that Tower is closed. Another minute passes and they try to contact Tower again; I tell them the Tower is closed again; and they ask me what Runway is being used. I respond that we have been using XY all morning; but that we are doing a practice approach on Runway XX. The Aircraft Y says they are inbound from the west and will follow behind us for Runway XZ (yes; XZ; not XX - which does not exist). I announce 6 mile final. The Aircraft Y nears the airspace and announces 'traffic; anyone in the airspace; please advise'. I call my position on final again. The Aircraft Y states they will setup for a left downwind entry for Runway XY. I listen to the weather and inform the Aircraft Y that the winds have shifted to 210 now and therefore XX would be the preferred Runway. The Aircraft Y responds and says they will still make left downwind for [Runway] XY. I announce 2 mile final Runway XX. The Aircraft Y asks me for my position and I say I am above the numbers (just above the Runway). The Aircraft Y responds by saying they have me in sight and will be wheels down shortly. I then saw the Aircraft Y make what appeared to be a very short approach for [Runway] XY; directly ahead of me on [Runway] XX; right as my wheels touch down. I announce that I will try to be short on landing and exit at the first Taxiway (which I did). Before I can even begin to exit the Runway; the Aircraft Y touches down; as well. They exit at the first Taxiway on XY; and I exit at the first Taxiway on [Runway] XX. At parking; I see the pilots get out an elder man and a younger lady who I later find out is arriving to take her private pilot checkride.