  We prove the stability of entropy solutions of nonlinear conservation laws
with respect to perturbations of the initial datum, the space-time dependent
flux and the entropy inequalities.
  Such a general stability theorem is motivated by the study of problems in
which the flux $P[u](t,x,u)$ depends possibly non-locally on the solution
itself. For these problems we show the conditional existence and uniqueness of
entropy solutions.
  Moreover, the relaxation of the entropy inequality allows to treat
approximate solutions arising from various numerical schemes. This can be used
to derive the rate of convergence of the recent particle method introduced in
[Radici-Stra 2021] to solve a one-dimensional model of traffic with congestion,
as well as recover already known rates for some other approximation methods.
