Saying there is an average temperature is quite reasonable. The question is how useful that metric is, and it is useful for one thing - trends in weather and temperature. We do not need trillions of data points for this - Earth has 200 million square miles of surface area. If we put a weather station in each square mile, and take 1 measurement every day, we get 73bn data points. In reality, we do not need this many, because temperature does not wildly change every day, every square mile. The pre-industrial average temperature (the 1850-1900 average) is not 0, be that °C, °F, or Kelvin (though I'll stick with Kelvin from now on because it's easiest). Average temperature was roughly 288K (15°C or 59°F). Now that has moved up to around 289-290K. This should be all I need to prove it's real, but let's continue.
78% of the atmosphere is nitrogen, 21% is oxygen and 0.9% is argon. These three are not greenhouse gases, as they have either one or no chemical bonds in their molecular structure. This leaves 0.1% of the Earth's atmosphere (by volume) to be greenhouse gases, or 1,000ppm. Space's temperature is around 3K, meaning those 1,000ppm greenhouse gases heat the Earth from 3K to 288K, or by 285K. Basic maths tells us that 1ppm of greenhouse gas causes 0.29K of temperature increase. Now, the reality is lower than this for a variety of factors (the sun heats up the space around Earth slightly, the gases only insulate at night, etc). So yes, 50ppm does mean a significant increase.
The law of equilibrium is correct. An infrared photon leaving the Earth strikes a CO2 molecule, exciting one of its electrons. That electron de-excites, emitting another infrared photon. That photon has a 50/50 chance of going back to Earth or into space. Without the CO2, it had a 100% chance of leaving Earth. Hence heating.
I'm not sure what greenhouse CO2 concentration has to do with anything, given that it's done because plants use CO2 in photosynthesis.
Now I would really love to see NASA's imagery of 3000ppm, if you could send that, please do. Same goes for your paper, I would love to read it. I would also love to hear about the statisticians who say satellite data is unreliable, especially since statisticians dont usually concern themselves with the workings of satellites.
As for your claim regarding geological periods, it is true. However, humans did not evolve in the Carboniferous period (300mya). We are not suited for different temperatures. Life will go on. Human life won't.