  We consider full non-Abelian, Abelian and center projected lattice field
configurations built up from random instanton gas configurations in the
continuum. We study the instanton contribution to the $\bar{Q}Q$ force with
respect to ({\it i}) instanton density dependence, ({\it ii}) Casimir scaling
and ({\it iii}) whether various versions of Abelian dominance hold. We check
that the dilute gas formulation for the interaction potential gives an reliable
approximation only for densities small compared to the phenomenological value.
We find that Casimir scaling does not hold, confirming earlier statements in
the literature. We show that the lattice used to discretize the instanton gas
configurations has to be sufficiently coarse ($a \approx 2\bar{\rho}$ compared
with the instanton size $\bar{\rho}$) such that maximal Abelian gauge
projection and center projection as well as the monopole gas contribution to
the $\bar{Q}Q$ force reproduce the non-Abelian instanton-mediated force in the
intermediate range of linear quasi-confinement. We demonstrate that monopole
clustering also depends critically on the discretization scale confirming
earlier findings based on monopole blocking.
