This is in pilotspeak, so probably not as technical as you want.

1) There is no real realtionship. The troposphere is narrower at the poles and wider at the equator.

2) Temp inversion is a low to the ground effect, usually from a clear night with calm winds. The cooler air, because of its greater density, settles close to the ground, and the warmer air forms a blanket above it in a temperature inversion. Thus, if you have winds, they mix the air and no inversion.

3) See above. You're now talking about temperature lapse rate. -2* C per 1,000 feet of altitude up from sea level. On a standard day, sea level is 15* C. Therefore, 3,000m or 9,900 feet is approximately -5* C ... on a standard day. There are many things that can change the temperature of a region, most important of which is the jet stream.

4) The ozone layer is in top of the stratosphere. The stratosphere is from 6 - 30 miles altitude.

5) There's lots of aerodynamics and fluid flow for Mach and the speed of sound. http://www.mathpages.com/home/kmath282/kmath282.htm Go here.