Also i have a crack in the exhaust manifold but i don't see how that could affect the throttle or the Mpg.

n general both of theses codes are very similar and often in foreign vehicles are thrown together. They in essence mean almost close to the same thing. P0171 (a generic code for almost every car) means that your oxygen sensor on bank 1 (if you have a V6, bank 1 is the side with cylinder #1, if an inline 4 or 5, bank 1 is the sensor closest to cylinder 1, usually on Hondas, there will only be 1 sensor so it's pretty straight forward) has had low voltage for a period of longer than 1 minute after the exhaust had fully warmed up. This tells the ECM that you have a Lean Air/Fuel ratio which can cause surging at idle or when you press the throttle, the car leaps forward... etc.. P0170 is again, basically the same, the ECM has detected a Lean Air/Fuel ratio. I would start out by cleaning the MAF sensor and throttle body, years of use can cause a lot of grime buildup and can set up these codes. Also, check all vacuum hoses to make sure none are missing, unplugged, cracked, etc... Check the PCV valve and make sure it is not covered/ filled with oil, or stuck open. this can cause oil to get into the intake and can damage your o2 Sensors, catalytic converter, MAF sensor, etc.. also check for exhaust leaks between engine and first o2 sensor (bank 1). Make sure you have a clean air filter. if it continues, fuel filter. a clogged fuel filter and make it really hard for the engine to get the perfect Air/Fuel ratio. then take the longest flat head screwdriver you have, start the car, and position the end of it on the top of each fuel injector and listen at the other end, it should be a very rhythmic clicking sound from each one and they should all be similar. some may be louder than others but that is because you will have the screw driver positioned differently on each one. you are trying to see if any of them sound like they are missing, not firing, firing slower than the others, etc... After you have crossed out all of this, then I would replace the o2 sensor. just make sure you rule everything out before you replace the sensor. if any of the above caused the old sensor to go bad, then the new one will too!