Since it's an auto it shouldn't be the NPS, the gearbox senses neutral differently. Here's something to try: handbrake on, engine off, ignition on, put the car in Drive, then try starting it. If it starts, the gearbox isn't detecting neutral properly. Put it in neutral - if it starts ONLY in neutral (or park) then it's sensing neutral properly.
I don't know if EGR is completely inactive in reverse (that would make sense, since reverse is almost exclusively for low-speed operation). An abundance of EGR will cramp the engine's power, if the EGR valve is opening more than it should. Find out by copying the gasket on the intake side of the gold EGR pipe but don't make the large hole (you're making a blanking plate). 1mm stainless, 2mm mild steel, 3mm aluminium should do fine. If blocking the EGR works then the valve is malfunctioning - replace it if you wish, but the engine won't need it for normal operation.