  We prove an optimal one-volume Wegner estimate for interacting systems of $N$
quantum particles moving in the presence of random potentials. The proof is
based on the scale-free unique continuation principle recently developed for
the 1-body problem by Rojas-Molina and Veseli\`c \cite{RM-V1} and extended to
spectral projectors by Klein \cite{klein1}. These results extend of our
previous results in \cite{CHK:2003,CHK:2007}. We also prove a two-volume Wegner
estimate as introduced in \cite{chulaevsky-suhov1}. The random potentials are
generalized Anderson-type potentials in each variable with minimal conditions
on the single-site potential aside from positivity. Under additional
conditions, we prove the Lipschitz continuity of the integrated density of
states (IDS) This implies the existence and local finiteness of the density of
states. We also apply these techniques to interacting $N$-particle
Schr\"odinger operators with Delone-Anderson type random external potentials.
