Also, What is the relationship between increased altitude pressure and temperature.
The relationship is not direct, as altitude increases, at first temperature decreases linearly, but around 11,000 feet it stabilizes, and at higher altitudes it begins to increase. Once you reach very high altitudes it begins to cool again.
The pressure at high altitudes decreases much more predictably. the pressure is a function of the density of the fluid (air), the gravitational constant, and the distance from the very top of the atmosphere. It decreases essentially linearly as you increase altitude.
High atmosphere fluid characteristics are somewhat difficult to model, within all functional altitudes you can find table listing pressure, temperature, viscosity etc.