Three-dimensional laminar hypersonic boundary-layer flows are investigated applying the compressible bi-global linear stability theory (B-LST) in flow crossplanes. The flat-plate flow is altered by an obliquely placed discrete fence-like roughness element that is about half the boundary-layer thickness high. Roughness setup and flow conditions resemble the STS-119 flight experiment. A cold-flow case and hot-flow cases are considered. The influence of non-perfect gas properties such as variable chemical composition, or thermal energy relaxation are included. The steady base flows are extracted from Navier-Stokes simulations. The underlying gas modell for reacting and non-reacting air accounts for thermal as well as chemical nonequilibrium. Rarefaction effects are considered in terms of a slip condition for velocity and temperature at the wall. Stability properties of the roughness wake under cold, hot, and hot rarefied flow conditions are compared in terms of local and integral growth.