Start and stall with throttle input is an immobiliser fault.
Start and keep running with throttle input, sounds like a throttle body assembly fault,does it compensate for loads when the car is running? AC / lights etc.Is the idle low at aorund550/ 600rpm when hot. and not at 750-800? if so, thorttle body fault. Don't just replace it,
have it tested by a VW specialist.