We present a continuation of an analysis that aims to quantify resolution of $N$-body simulations by exploiting large (up to $N=4096^3$) simulations of scale-free cosmologies run using \Abacus. Here we focus on pairwise velocities of the matter field and of halo centres selected with both the Rockstar and CompaSO algorithms. For the matter field, we find that convergence at the $1\%$ level of the mean relative pairwise velocity can be demonstrated over a range of scales, evolving from a few times the grid spacing at early times to slightly below this scale at late times. Down to scales of order the force smoothing, convergence is obtained at $\sim5\%$ precision, and shows a behaviour indicating asymptotic stable clustering. We also infer for LCDM simulations conservative estimates on the evolution of the lower cut-off to resolution (at $1\%$ and $5\%$ precision) as a function of redshift. For the halos, we establish convergence, for both Rockstar and CompaSO, of mass functions at the $1\%$ precision level and of the mean pair-wise velocities (and also 2PCF) at the $2\%$ level. We find that of the two halo finders, Rockstar exhibits greater self-similarity, specially on small scales and small masses. We also give resolution limits expressed as a minimum particle number per halo in a form that can be directly extrapolated to LCDM.