We started sending radio signals in an appreciable amount somewhere around the 1920-1930s, and have since made our radios so efficient (also with the help of satellites) that by now they are basically too weak to be realistically noticable by distant civilizations.
Given that we started about 100 years ago, those radio signals only traveled 100 light years (enough to reach quite a few solar systems, but only about 0.1% of the radius of the milky way).
We don't know quite how good alien civilizations are at signal processing, but beyond 1000 light years or so it will be seriously hard to seperate our broadcasts from random noise. So not quite 3 billion light years.
No, they aren't. This is an approximation taught to you in high school to make certain problems more tractable. You've got at least two methods of generating non-spherically-expanding EM waves sitting in your pocket right now; neither your phone's screen nor its flashlight are perfectly spherical in emission. This is trivially observable by the fact that the orientation of the phone impacts your perception of its brightness.
It's true that you can't make a "fully" directional EM wave with no spread whatsoever, but you can make it arbitrarily small with engineering effort, and they're trivially not spherical.
https://en.wikipedia.org/wiki/Gaussian_beamI don't think anything from Earth will be detectable beyond more than a few light years.
https://en.m.wikipedia.org/wiki/Parabolic_antenna
I think we generally believe that the dishes are used just for receivers but they are also used in directing transmitters.
In fact, there are also heavy regulations for high-speed long distance directed microwave antennas to not spread the signal too broadly:
https://www.fcc.gov/Bureaus/Engineering_Technology/Orders/19...
https://www.popularmechanics.com/space/news/a27934/galaxy-ma...
If we can control the amount of energy as these broadcasts, we'd basically be gods for all intents and purposes.