Should temperature and pressure conditions for two reactions be same for them to combine for enthalpy calculations?
yes they should be for a simple reason: when you do make C and S react together  you are going to assume that the temperature and the pressure of the box you're using for the reaction is the same. In particular you can even think of putting for example the hot solid in the box with the cold gas, when you're talking of entalphy of formation you're basically speaking of the equilibrium situation. You will reach equilibrium only once al the macroscopical quantities are perfectly equal in all the box you're working with. If this was not the case, the equations you would have to solve are much more complicated than those you are usually seeing .