Regarding air vs. nitrogen (or CO2), you don't really need to figure out the answers to all the questions you ask. In the end the only question that matters is if N2 or CO2 will result in less cal-constant change than air for a given temperature change. To test that, you just need to fill your tire with air early in the morning, do calibration rides when it's cool, and then again a few hours later when it's warmer. And then repeat that on a different day after you fill the tire with N2 or CO2.