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Sorry for the delay in response.

The simple answer to the question is that shit, and effluents derived from it, will flow down hill. The rate at which this will happen, and hence the level of risk to the stream or to surrounding water sources will depend on the nature of the soil. As far as I am aware all the theories regarding the reduction of pathogen numbers in the effluent are dependent on the speed of the flow though the porous soil media. Provided that the effluents are about a metre above the water table travel through the unsaturated zone should be slow and hence a high degree of die off should occur as the head to drive the flow in the unsaturated zone will be derived slowly from the depth of the effluent in the pit. If the effluent forms a hydraulic connection with the water table then the effluent will be transported at the same rate as the flow as that of the groundwater. It is not rally feasible to predict the concentrations that might reach the stream as the concentrations gradient will be affected by dispersion, dilution and natural remediation. The impact of the stream will depend obviously on the volume flow rate of the stream. The higher the flow rate the lower the risk of significant contamination as concentrations are reduced through dilution and the natural attenuation processes of the stream will occur quite quickly. Given the description of the site I would say that it is quite likely that the stream is hydraulically connected to the groundwater system in the area.

An added complication is the presence of macro-pores or soil pipes that are often formed in the subsurface on hill slopes. If these are present then flow will be governed by the open channel flow regime rather than Darcy’s law and zero remediation can be expected. I mention this because I am aware of at least one situation where pit latrines on hill slopes were implicated as the most likely source of contamination of a spring at the bottom of a hill slope, located quite a significant distance from the pits. This contamination was responsible for an outbreak of typhoid amongst the community using the spring (and the pit latrines).

From the description given I would say that there is a low to medium risk of the effluent reaching the stream, provided that the water table in the area is well below the bottom of the pit. This risk is non-negligible, and the potential associated impacts depend on whether or not the water in the stream is used for bathing or for consumption without treatment. Perhaps the best approach would be to consider using a septic tank/aqua privy system connected to a system of French drains to disperse the resulting effluent? I would be relatively unconcerned about the potential impacts on the farmland. I think the chances of seepage from the pit emerging at the surface in a volume that would affect the land is relatively low. For an overview of the potential adverse impacts of this on the farmers land or crops you could check out https://www.who.int/water_sanitation_health/wastewater/gsuww/en/

I hope this was helpful rather than confusing.

Best regards

John C