You are going to need a sensor that extends out into the combustion chamber, otherwise it will primarily just read the temperature of the walls, which will have a very large thermal inertial and not change nearly as fast as the gas temperature will. Similarly, you will need a very high frequency response because presumably your pulses are likely short. Combining that with the high temperatures will be... problematic. I know type G, C, and D thermocouples from Omega (which are not industry standard designations) can go up to something like 2300°C, which is likely close enough. They don't likely have high frequency response, though it might be worth a try. Otherwise you are probably stuck with some of the more standard thermocouple types which might have high-speed varieties (I know they exist for type E) and you just will perhaps have a lot of measurement error at your high temperatures.
As for pressure, The highest temperature I saw in a (very quick) Google search was ~400°C. Basically, what you will have to likely do is get a high-frequency pressure transducer and find a way to keep it cool. I suspect that won't be a problem due to the fact that your pulse times are likely so short that very little thermal energy is likely transferred to the transducer.