Comprehensive knowledge of physical properties such as equation of state (EOS), proton exchange, dynamic structures, diffusion coefficients, and viscosities of hydrogen-deuterium mixtures with densities from 0.1 to 5 g/cm^{3} and temperatures from 1 to 50 kK has been presented via quantum molecular dynamics (QMD) simulations. The existing multi-shock experimental EOS provides an important benchmark to evaluate exchange-correlation functionals. The comparison of simulations with experiments indicates that a nonlocal van der Waals density functional (vdW-DF1) produces excellent results. Fraction analysis of molecules using a weighted integral over pair distribution functions was performed. A dissociation diagram together with a boundary where the proton exchange (H_{2}+D_{2}⇌2HD) occurs was generated, which shows evidence that the HD molecules form as the H_{2} and D_{2} molecules are almost 50% dissociated. The mechanism of proton exchange can be interpreted as a process of dissociation followed by recombination. The ionic structures at extreme conditions were analyzed by the effective coordination number model. High-order cluster, circle, and chain structures can be founded in the strongly coupled warm dense regime. The present QMD diffusion coefficient and viscosity can be used to benchmark two analytical one-component plasma (OCP) models: the Coulomb and Yukawa OCP models.