Biochar was prepared by the hydrothermal carbonization (HTC) of palm leaves, characterized, and utilized as an adsorbent for Malachite Green dye (MG). The Higher Heating Value (HHV) of biochar depends on the carbonization temperature and has a maximum value of 24.81 MJ/kg. Activation using H₂O₂ oxidation of HTC biochar prepared at 208 °C produced AHTC with improved capacity. The optimum pH was found to be in the range 7–8. Freundlich, Langmuir, Temkin, and Dubinin–Radushkevich adsorption isotherms were used to study MG adsorption data. The Langmuir isotherm provided the best fit for experimental data. Experiments conducted using activated biochar AHTC at 25 °C resulted in an adsorption capacity of 62.80 mg/g, far greater than what was observed for HTC biochar (45.59 mg/g). The maximum adsorption capacity was 88% when the concentration of MG solution was 66 ppm. The free energy change in adsorption DG° indicated that the adsorption process was spontaneous. Adsorption followed pseudo-second-order kinetics. Fixed-column adsorptions models, namely, Thomas, Yan et al. and Yoon–Nelson models, were investigated for AHTC. The column adsorption capacity determined by the Thomas model was 33.57 mg/g. In addition, a computational investigation has been carried out to determine the structural and electronic features, as well as the quantum chemical parameters of HTC and MG. Moreover, the interaction between the HTC and MG is investigated, which is further elaborated by performing non-covalent interaction (NCI) through the reduced density gradient (RDG) analysis. Thus, the easily prepared hydrochar from abundant waste palm leaves can be used as a high-value biocoal and efficient adsorbent of the cationic dye malachite green.