That's a good choice of wording :) It may or may not apply, it depends on the antenna.

The physical basis for all inverse square laws - gravity, electrical charge attraction, radio signal strength, is actually geometric. They are all measurements of some kind of flux, so you have a certain quantity of signal, which then has to be divided by the surface area of the sphere surrounding the source. As the distance from the source increases, the surface area of the sphere increases as the square of the radius.

So yes, if the source is in fact a point source radiating equally in all directions, the signal drops off as per the inverse square law. But, if you have a very tight beam, then the signal strength is maintained for a lot longer. In that case, signal loss is caused by diffusion, and by attenuation due to hitting matter that is in the beam. A highly parallel laser beam of a not unreasonable power level, preferably generated from a satellite orbiting outside any atmosphere, should be capable of being received pretty much anywhere in the galaxy. Alternatively, if you have a big enough dish, you could do the same thing with radio waves. Indeed, it is estimated that Arecibo is capable of communicating with any other Arecibo-style dish in a roughly 100 hundred light year diameter around the Earth, if the two happen to be pointed at each other, and one is transmitting whilst the other is receiving... http://www.cplire.ru/html/ra&sr/irm/limitations.html

And that's with a measly 1000kW radio, weaker than most primary radars used today.

We can detect quasars billions of light years away because they are big mothers, but really hard to modulate, and turned off by now.

They address this under "No More TV for Aliens". CTRL-F for it.

Also: yes the inverse square law does apply to radio waves.

I don't understand why not. Aside from the difference in wavelength, there's absolutely no physical difference between radio waves and physical light.