The usage of direct numerical simulations for research of turbulent combustion for space propulsion applications is explored. With this goal in mind, the combustion near the injection of a fuel-rich methane-oxygen flame at 20 bar is simulated using a massively parallelized solver. The statistical properties of the relevant physical fields are examined to study interactions between turbulence and combustion. This analysis is complemented by an investigation and quantification of the error sources in direct numerical simulations of turbulent diffusion flame. A method to estimate the statistical error is derived based on the classical inference theory. In addition, critical resolution criteria are discussed using a mesh sensitivity analysis.