Hi
Regarding the earth strap, these are impossible to test without specialised equipment as their resistance should be only about one thousandth of an ohm. They may look OK, and you can clean the end lugs till they are shiny, but hidden between the crimp and the braid is a layer of corrosion. Replacement is best.
I think your next step would be to get the van scanned for stored error codes. Not all errors result in a dashboard warning light, so there may be some which you would otherwise be unaware of. Error codes remain stored indefinitely until they are cleared. The ideal thing to use is a Fiat specific scanner as used by dealers, or
MultiECUscan which is available to amateur mechanics - at a price. However, even a lower cost fault scanner will give some functionality for reading generic codes.
Do you happen to know if the Throttle Body (TB) has ever been changed ? The factory fit for 2008 was a unit made by Wahler, which have proved rather unreliable over time. Better replacements are available e.g. Marelli. The TB sits at the front of the engine with a big curved aluminium pipe leading down onto the inlet manifold. If you take off the large rubber air hose leading into it, you can see the throttle disc (= flap valve). especially if you use a small mirror. Try gently moving the disc with your fingers to check for sticking - it should move smoothly. It is designed to be sprung nearly closed, and the electric actuator solenoid should pull it open it as required. If the flap doesn't open enough, the engine is starved of air and power will be restricted. However, the air flow at idling is fairly small, so it would need to be almost completely closed to cause the engine to cut out. At Idling and low power there is little boost from the turbo, so running the engine with the rubber inlet hose disconnected will not alter conditions much. It's possible to watch the action of the throttle disc. See whether disc movement correlates with the engine cutting out.
Please note that I am advising basic checks, I'm not suggesting you rush out straight away and spend money getting the TB changed and then curse me when it turns out to be something different !