First of all, let me start by saying that you have some good questions.
When considering oxidant (air and/or oxygen enriched air) as an ideal gas, its enthalpy value is a function of temperature only. Therefore, there is no pressure dependency when doing an energy balance and trying to calculate the combustion products flame temperature where the enthalpy value of reactants (fuel + oxidant) is equal to the enthalpy value of combustion products for given stoichiometry value (oxidant to fuel ratio).
However, when doing more time consuming and more computing complex calculations for the purpose of determining the combustion products flame temperature based upon the minimization of the Gibbs free energy, then the pressure becomes one of the input variables. In general, the higher the pressure value, the higher the combustion products flame temperature value. Again, such calculations cannot be done by hand and require good software and computer tools and resources.
In my opinion, combustion pressure of 70 [bar] and/or 70 [atm] is too high. Gas turbine combustion takes place around 15 [atm]. With high pressure, there are many issues that need to be considered and addressed for reliable and safe operation of such combustion equipment.
In atmosphere, one can always find standard air, which is on mole (volume) basis 79 [%] nitrogen and 21 [%] oxygen while on weight basis 77 [%] nitrogen and 23 [%] oxygen. Molecular weight for nitrogen is 28 [kg/kmol] and for oxygen is 32 [kg/kmol] resulting that air molecular weight is 29 [kg/kmol].
Therefore, it is easier to change the oxidant to fuel ratio by changing the amount of fuel getting to the combustor -- for the gas turbine operation, the amount of air is pretty much steady, while by changing the amount of fuel one controls the combustion products flame temperature.
As far as I know, when using methane as the fuel and standard air as the oxidant at stoichiometric combustion conditions, the combustion products flame temperature is ~ 2,300 [K]. Gas turbine operation requires that the operating conditions at the inlet of the gas turbine are: ~ 15 [atm] and 1,500 [K] -- meaning that the oxidant to fuel ratio is much higher than what is required for the stoichiometric combustion conditions.
One can change the oxidant composition, but an air separation unit is required to have oxygen enriched air as the oxidant -- compression is required ...
Here are a few combustion plots for stoichiometric conditions:
Here is a URL providing some engineering/technical background information related to the combustion process for stoichiometric conditions:http://www.engineering-4e.com/components.htm
Here is a URL for an online calculator for stoichiometric combustion of various fuel and oxidant compositions providing what the combustions products composition on both weight and mole (volume) basis is: http://www.engineering-4e.com/calc4.htm
I do hope that my input will be of some help to you.