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you need to tell us which codes are coming up, by the number. Youre probably getting a code for just a bad Mass Air Flow sensor, $250-400? for a stock new one, or you could be gettin a code for the Relays which you can get for $15-20 for both. If you have to replace the sensor then go ahead and get the relays because theyre probably bad too, MAF and relays cause each other to go bad.
Fix the burn-off relay problem first. It may fix the MAF low readings.
Replace the MAF burn-off relay remove the bellows from the front of the MAF, with a mirror verify that the sensor wire glows red for 2 sec after turning off the motor.