  We consider symmetric partial exclusion and inclusion processes in a general
graph in contact with reservoirs, where we allow both for edge disorder and
well-chosen site disorder. We extend the classical dualities to this context
and then we derive new orthogonal polynomial dualities. From the classical
dualities, we derive the uniqueness of the non-equilibrium steady state and
obtain correlation inequalities. Starting from the orthogonal polynomial
dualities, we show universal properties of n-point correlation functions in the
non-equilibrium steady state for systems with at most two different reservoir
parameters, such as a chain with reservoirs at left and right ends.
