I know it was a few years ago that this was posted but I had something similar just after Christmas 2020. I have a 500x 1.4 multi air turbo and I had just got a service done and, the week after, timing belt and water pump too. After a few days, the car stuttered and spluttered on starting. All fault lights and warnings on. Took it to fiat (in the UK) and they couldn't find anything wrong, no codes had been saved either. Couple of days after, the car engine stopped as I was driving around a roundabout, not a very nice feeling. Got towed to the fiat dealer again and they couldn't find a fault but it wouldn't start. They had some codes though. And when they tested the car, the same thing happened to them. They asked fiat in italy and the answer came back for faulty crankshaft sensor. They had to order the part from italy (not in stock in the UK) then they found a fault with the wiring to the sensor so they changed that too. Got my car back after about 2 weeks today, let's hope that this has cured it. Car drives well now, fingers crossed.
I hope this helps someone else with similar problems.