Single engine pilot with an instructor reported a critical ground conflict while on the runway and during taxi. The conflicting aircraft landed and followed the pilot's aircraft closely down the runway. The pilot states; after pulling off in the run-up area; the other aircraft did not follow the center taxi line but taxied across the grass to the fuel pumps to let passengers off.

Narrative

My instructor and I returned from a practice area following the Runway X corridors per the FOM. We entered a 45 to downwind for Runway X making a radio call. Entered a downwind for Runway X making a radio call. When we are abeam the numbers we hear a transient aircraft make a downwind radio call; he had not made a 45 to downwind call. We proceed to tune base; making a radio call and hear the other aircraft make a base call as we are still in the base. We then call our final turn and proceed to land on Runway X going full length. As we were rolling down the runway I looked behind us to discover the other aircraft on the runway at the same time as us (within 500 feet) and moving faster than we were. When we were clear of the runway I made the decision to taxi into the run-up area for the after landing checklist so he could clear the runway as well. I complete the after landing checklist and observe the aircraft taxi by us with excessive speed. We then proceeded to taxi behind him and observe him park in the first T spot near the grass. After we pass him on the ramp; he recklessly proceeds to taxi towards the fuel pumps not following the center line; cutting through the grass; and putting the nose/propeller of his aircraft within 3 feet of the fuel pumps. He quickly proceeded to shut down the airplane; unload his passenger; push back the airplane; and depart the airport with haste.