The Mass Air Flow (MAF) senses the amount of air about to enter the engine, the Power Control Module (PCM) uses this data to adjust the fuel supplied to the engine. If the reading is out of range (Low for example) it will cause the domino of events noted by your trouble codes when the fuel pressure is lowered the fuel supplied is lowered and the turbo in turn will not produce as much boost because it depends on exhaust temperature to produce full boost pressures, so the botXXXXX XXXXXne is the MAF code is the relevant issue. the PCM is not receiving the proper signal voltage and is adjusting accordingly. So to diagnose the MAF problem a quality scan tool can read the MAF sensor output in grams per second, at idle fully warmed up it should read approximentaly 4.0 to 9.0 grams per second. When the engine is accelerated the values should rise quickly with engine RPM and remain steady at a steady engine RPM.
First check the voltage supply and ground circuits by disconnecting the connector from the MAF sensor connect the Pos lead of the volt meter to the pink wire and the Neg lead to the Black/White wire. Turn the key "ON" and you should read approx. 12 volts. If there is no voltage, of course check ALL related fuses with a test light or meter first! Then check the ground by moving the Neg meter lead to a known good ground like the batt.
It is also possible that the replacement MAF sensor has a problem, but the scan test mentioned above will verify this. But it is critical to test the power and ground circuits for a complete diagnosis!