Given a finitely generated group G, a non-trivial element g\in G, and a minimal action of G on a compact space X, with amenable neighborhood stabilizers, we prove sufficient conditions in terms of various growth/decay functions for topological freeness of the action of g on X. We apply our results to the case of the (Furstenberg) boundary action of G, to conclude C*-simplicity under (sub)rapid decay conditions. In this context, we also give a description of the support of stationary states on the reduced C*-algebra of G. This is joint work with Nazmul Alam, Joseph Gondek, and Randy Pham.