C172 Flight Instructor conducting operations at a non-towered airport reported NMACs and ground conflicts with two agricultural aircraft operating in and out of the airport.

Narrative

I was conducting a practical test with a private pilot applicant. While conducting the traffic pattern and landing areas of operation required by the Airman Certification Standards; I encountered multiple runway incursions and a close near miss by 2 Air Tractor 802 aircraft. Aircraft Y and Aircraft Z were operating off of the ZZZ and conducting aerial application operations within 3 nm of the airport. These aircraft; particularly Aircraft Y; entered and left the airport in a very aggressive and rushed manner. Multiple times the aircraft landed on the runway behind us while we were still on the runway. In one of the encounters Aircraft Y exited the runway and blocked our path to exit the runway and we had to remain in the runway safety zone while another aircraft was waiting to take off. Either Aircraft Y or Aircraft Z passed beneath our aircraft's flight path while we were on the upwind leg after taking off from the runway. I estimate that the vertical distance was around 100 feet. Finally; on our final landing one of the aircraft announced that they were going to line up and wait in the opposite direction while we were on our landing roll out. The aircraft then proceeded to takeoff prior to our aircraft exiting the runway safety area. Lining up and waiting at a non-towered airport is dangerous enough; let alone with an aircraft on landing roll out on the runway in the opposite direction.I realize that these agriculture aircraft operators are under pressure to complete their flights in a timely manner. I know the importance that ag [agriculture] aircraft have on the farming community. However; these operations are injecting risk to non-participating aircraft with their airport operations. 14 CFR 137.45 allows these operators; the nonobservance of airport traffic pattern. There are some caveats that I do not think that the operators are following. 137.45(a) Prior coordination is made with the airport management concerned. After landing; I asked the airport management who the ag operator was on the field and they replied they didn't know. They had not checked in with airport management. 137.45(b) Deviations are limited to the agricultural aircraft operation. 137.3 defines 'agricultural aircraft operation' as means the operation of an aircraft for the purpose of (1) dispensing any economic poison; (2)dispensing any other substance intended for plant nourishment; soil treatment propagation of plant life; or pest control; or (3) engaging in dispensing activities directly affecting agriculture; horticulture; or forest preservation; but not including the dispensing of live insects. While departing the airport with a load and returning for reload I can see that they are engaged in 'agriculture aircraft operation'; but when ferrying into or out of the field they operate in the same manner and it seems they are not meeting the definition of 'agriculture aircraft operations' in those scenarios. 137.45(d)The aircraft at all times remains clear of; and gives way to; aircraft conforming to the traffic pattern for the airport. Clearly these operators are not remaining clear of or giving way to aircraft conforming to the traffic pattern. I have had more 'near misses' with ag aircraft operating out of ZZZ than in any of my previous experiences. I don't have a solutions to this issue other than restricting ag operations if they cannot only comply with the CFRs; let alone good risk management practices.