Metallic materials are widely used in industrial applications due to their excellent electrical transport properties and superior thermal dissipation performance. However, experimental measurements of electrical and thermal conductivity under high-temperature and high-pressure conditions are challenging and costly. This makes numerical simulation an efficient alternative. In this study, we developed a computational software named TRansport at EXtremes (TREX). It is based on the Kubo-Greenwood (KG) formula combined with first-principles molecular dynamics. This software is used to calculate electrical conductivity and electronic thermal conductivity. Using magnesium and magnesium-aluminum alloy AZ31B as research subjects, we systematically investigated their electrical and thermal transport properties. The temperature range was 300~1200 K, and the pressure range was 0~50 GPa. The methodology involved employing first-principles molecular dynamics simulations to obtain equilibrium configurations of high-temperature disordered structures. Electrical conductivity and electronic thermal conductivity were calculated using the KG formula. Lattice thermal conductivity was determined via the Slack equation. To validate the reliability of our approach, we performed comparative calculations using the Boltzmann transport equation (BTE). The results were cross-verified with experimental data from Sichuan University and the Aerospace Materials Testing and Analysis Center. The findings demonstrate that the maximum relative error between computational and experimental results is within 20%. This confirms the accuracy of our method. Additionally, we elucidated the variation patterns of electrical and thermal conductivity in magnesium and AZ31B alloy with temperature and pressure. These patterns include the reduction in electrical conductivity due to aluminum doping, the significant enhancement of conductivity under high pressure, and the unique temperature-induced thermal conductivity enhancement in AZ31B alloy. The TREX program developed in this study and the established performance dataset provide essential tools and data support. They are useful for research on electrical and thermal transport mechanisms in metallic materials under extreme conditions, as well as for engineering applications. The dataset supporting this article can be accessed and obtained from the Science Data Bank repository at https://www.doi.org/10.57760/sciencedb.j00213.00128. (During the review stage, please access the dataset via the private access link: https://www.scidb.cn/s/jA7rq2.)