Aerothermodynamics is an integral component in the design and implementation of hypersonic transport systems. Accurate estimates of the aerodynamic forces and heat transfer rates are critical in trajectory analysis and for payload weight considerations. The present work seeks to investigate the ability of an unstructured Cartesian grid framework in modeling hypersonic viscous flows. The effectiveness of modeling viscous phenomena in hypersonic flows using the immersed boundary ghost cell methodology of this solver is analyzed. The capacity of this framework to predict the surface physics in a hypersonic non-reacting environment is investigated. High velocity argon gas flows past a 2-D cylinder are simulated for a set of freestream conditions (Reynolds numbers), and impact of the grid cell sizes on the quality of the solution is evaluated. Additionally, the formulation is verified over a series of hypersonic Mach numbers for the flow past a hemisphere, and compared to experimental results and empirical estimates. Next, a test case that involves flow separation and the interaction between a hypersonic shock wave and a boundary layer, and a separation bubble is investigated using various adaptive mesh refinement strategies. The immersed boundary ghost cell approach is tested with two temperature clipping strategies, and their impact on the overall solution accuracy and smoothness of the surface property predictions are compared. Finally, species diffusion terms in the conservation equations, and collision cross-section based transport coefficients are installed, and hypersonic flows in thermochemical nonequilibrium environments are studied, and comparisons of the off-surface flow properties and the surface physics predictions are evaluated. First, a 2-D cylinder in a hypersonic reacting air flow is tested with an adiabatic wall boundary condition. Next, the same geometry is tested to evaluate the viscous chemistry prediction capability of the solver with an isothermal wall boundary condition, and to identify the strengths and weaknesses of the immersed boundary ghost cell methodology in computing convective heating rates in such an environment.