About the problem 1:
I just calculated the free-energy (ΔG°) of the combustion of methane and i got a negative number, which would mean the reaction is favored or spontaneus in the direction the reaction was done.
CH4 + 2O2 ---> CO2 + 2H2O
Conditions for spontainity are equilibrium in temperature and constant pressure.
About problem 2:
Is it possible to resolve this problem with this equation Q=msΔT?