No, ULF is an antenna system, but because it is electrically very much shorter than a wavelength at the frequency in question, the impedance is very high, and the coupling efficiency is very low. You need MW of power put in to get a few dozen watts of radiated power, but that signal does cover the entire planet though, penetrating to a few kilometers down even in the ocean, enough to be detectable with a long wire and sensitive receiver.
SWER is using the random conduction path in a mix of soil, ground water to provide a somewhat lossy conductor for electrical power transmission at high voltage. The voltage drop can be a few hundred volts at full load, but it is cheaper to make the connection and maintain it than to build a 2 wire high voltage line to make a metallic 2 wire circuit.
Telegraph the same, cheaper to run one long cable to each side and have a ground return than to add the extra wire and insulators to provide the second.
Earth ground is there to provide a common reference voltage, nothing special, just a defined point that will be roughly the same for all points nearby, and thus a common way for all voltage sources to be roughly the same potential difference from each other. Nothing special, it is a big connection that has some poorly defined resistance, somewhat variable reactance, has roughly the same potential in an area and is a convenient point to use.
In power use it is there for safety, providing a way for there to be low voltage differences between the houses in an area, and to keep insulation from exceeding the rated voltages if the one line that is not referenced floats higher in voltage relative to ground for some reason. thus all power cables have some earth reference by some means, generally using a point on a transformer winding that is deemed to be the earth protective point.