Student pilot with Flight Instructor reported two critical ground conflicts with an aerial applicator aircraft at a non-towered airport. The aircraft attempted to land on the same runway the student's aircraft was on; then after going around overflew them and landed on runway while student aircraft was still on the runway.

Narrative

My CFI and I landed on Runway XX after completing a standard traffic pattern with appropriate and accurate radio calls about our position at the time before the incident occurred. After coming to a stop where the grass runway; XY/XZ; meets XA/XX; we announced back taxi over the radio and as we come around facing a XXX heading for back taxi to the beginning of Runway XX; we see a crop-duster on short final for Runway XX. Immediately; we attempt to pull off the runway at the XY/XZ concrete extensions attached to XA/XX in order to avoid a potential meeting between our aircraft and the crop-duster. We hear over the radio that the crop-duster is going around and asking if we want to wait for him to land or if we are going to back taxi. Since we are still located on the active runway; XA/XX; we announce loud and clear that we are going to continue our back taxi to the start of Runway XX. As we have approximately 1;000 feet left to the beginning of Runway XX; we see the crop-duster turn final once again; unannounced; and continue a descent to the runway as we are back taxiing on the active runway. Instead of going around; the crop-duster overflies us at about 10-20 feet and lands behind us while we are still on the active runway. My CFI and I agreed that the actions of the crop-duster were grossly negligent and outright dangerous. It poses a significant hazard to flight safety and should be addressed for the safety of future flights.My CFI and I were following all known rules and regulations when conducting our traffic pattern and back taxi. We also provided accurate and clear radio broadcasts that were confirmed to be heard by the pilot of the crop-duster who responded over the radio. We believe this event was caused by deliberate and dangerous decision-making from the pilot of the crop-duster who decided to land on an active runway with our aircraft still having clear possession over that runway via radio-announced back taxi. At no point did we ever leave Runway XA/XX or announce that we were leaving said runway; so there shouldn't have been any confusion.I don't entirely know what we could do differently. Our plane had clear possession over the runway and the crop-duster should have gone around and waited for us to complete our back taxi prior to landing. We could have politely asked the crop-duster; after noticing that it wasn't aborting its approach to the runway we were actively on; to go around until we finished our back taxi. We also could've assumed the unpredictability of crop-dusters and elected to exit the runway onto the 'XY/XZ' grass strip; then held short until the crop-duster had landed and left the runway. Either way; we were within our rights to commence back taxi after landing on Runway XX and for the crop-duster to blatantly ignore that is unsafe and represents several hazardous attitudes.