The MAF sensor is the Mass Air Flow Sensor, located just after the air filter, and is a series of electronic components and is very susceptible to damage if cleaned with a toothbrush. If it has failed, it manifests itself by the engine not being able to rev under load. To test, disconect the plug on the top (you will get a warning on the dash) and see if it will run ok under load and the problem goes away (you may produce a lot of black smoke) if that happens the MAF has failed, if its dirty wash it off with Spray Brake and Clutch cleaner, if still no improvement you need a new one. This sensor controls the air to fuel ratio. As air passes the sensor it cools a component lowering the resistance and this is related to air flow. Included is also a temperature sensor for incoming air, which will effect changes for cold running until the engine warms up, such as the EGR opening allowing hot gasses into the air manifold without it going through the EGR cooler.
The MAP Manifold Absolute Pressure sensor, not Barometric pressure sensor, this could be elsewhere, not connected to the engine, may be incorporated with the Ambient air temp for the dash. MAP located lower lhs of inlet manifold. As the pressure in the manifold is relient on the turbo charger, then barometric pressue does not come into it.
The MAP may get carboned up as it is the manifold, but can be removed easy and washed off with C& B cleaner.
I have seen a utube video of oven cleaner being squirted into the intake manifold to dissolve the carbon, I suppose the MAP sensor location could used and the cleaner being left overnight to work.
The vacuum pump will be used mainly for the brakes and possibly for operating vacuum motor devices on the turbo.
Unless operating at high altitudes I very much doubt that barometric pressure affects the operation of the engine at sea level. Barometric pressure and temperature has an effect on the density of the air.
I will look up the operation of the MAP and report back. It may control the boost pressure required for rpm, fueling , load etc, this is guessing.