In regard to resetting your ABS lights - take full lock to one side, hold for a second, take full lock the opposite side, hold for a second, then centralise it. Drive slowly in a straight line for about 30 yards+ and the lights should go out. Otherwise a short drive will suffice.
About your fault, I'm really stuck as I never had an issue with my TDI like this. Early on it had to have a new ECU as it would not start, but never cut out when driving, it may need a bit of poking and prodding from a good independent garage.
Never heard of this before, but check operation of your intake flap motor (sits before EGR), if that is closing when it shouldn't then it will be starving the intake of air, a very long shot really.
Is it just the engine cutting out, or is there an electrical blackout too?
Does it judder and chug while shutting down?