This study has been performed to reveal the main characteristics of operating a direct current (DC) plasma-chemical reactor (PChR) designed for hazardous waste treatment. The PChR employs thermal plasma as the operating environment. The investigations presented in this paper were conducted to study the electrical and energy characteristics of the plasma torch and plasma-chemical reactor during the destruction of inorganic waste. The PChR is equipped with a plasma torch with a nominal capacity of 50 kW and a free-burning arc. The zone of heat release from the atmospheric pressure DC arc cathode and arc anode (melted waste) spot is combined with the area of chemical reactions. The plasma torch (PT) parameters vary in the range of arc current I = 120–180 A, arc voltage U = 250–280 V, arc length x = 0–100 mm, and gas flow rate G = 1–3 g/s at atmospheric pressure, using air as the plasma-forming gas. The experimental results confirmed that plasma technology has several advantages over conventional incineration, including higher temperatures, heat source independence from the waste being processed or additional fuel, and a shorter exposure time in the high-temperature area. It was determined that the arc current increases with increasing arc length. With increasing arc length, the initial part begins to operate in a turbulent regime. This study determines the dependence on the heat flux transferred by electrons to the anode on the arc current. The convective heat flux density distribution over the anode heating spot was measured and discussed.