Why does the author not add pressure of the freestream (static pressure for clarify) to the variables ? How does he know that pressure of the freestream not effect the aerodynamic force R?
Freestream static pressure is not an independent variable when both density and speed of sound are given already. Adding pressure will not improve the equation because it can be canceled out at a later stage.
Static pressure is everywhere. At the front of the wing where the air streams onto, but also at the back of the wing.
We're talking on an intuitive basis here, and we do realise that the denser the fluid, the higher the force. Lift will be higher in water than in air, it is 1000 x denser. But it does not increase if we go from 10 m below sea level (pressure = 2 bar) to 20 m deep (pressure = 3 bar).
Static pressure will become a factor when compressibility needs to ne considered, near transsonic speeds and above. How much the air is compressed does depend on static pressure. The analysis with density and velocity only holds for lower free stream speeds where the air can be considered incompressible. Indeed, point 5 takes this into account.
Friction drag of a fluid is caused by the viscosity of the fluid. According to Viscopedia, static pressure has a very small influence on the viscosity of fluids that may be considered as incompressible. Air at lower Mach number is usually considered incompressible.