A hydrocarbon resource recovery apparatus for a subterranean formation having a wellbore extending therein includes a radio frequency (RF) power source, a dielectric fluid source, and an RF antenna within the wellbore. An RF transmission line extends within the wellbore between the RF power source and the RF antenna and is coupled to the dielectric fluid source to be cooled and/or pressure balanced by a flow of dielectric fluid therefrom. A hydrocarbon resource recovery pump is within the wellbore and is also coupled to the dielectric fluid source to be powered by the flow of dielectric fluid therefrom.