This problem is exactly why i joined this forum, to get help and theres loads of it here.
I've just bought a fiat and I need help to on the same situation with a 1.2L 500c. Rough idling and stalling. somehow, I think I might have solved my problem, but not 100% sure yet.
Loads of things could be wrong, faulty coil pack, vaccum leaks, spark plugs even low oil pressure, the list goes on and on. So for me, an OBDII reader shows no fault, even after its stalled. so I force it to fault (not sure how safe this is, so DO NOT copy me. this is the risk I am taking and could damage the engine even more), I turn off the engine and unplug the Cam shaft position sensor and restart the engine and it seems to run smoother and doesn't stall, but the engine management light will come on and show a P0010 Fault on the OBDII reader. I turn off the engine and replace the electrical plug and we're back to rough idling and stalling. So I've ordered a new cam shaft position sensor and we will see what happens after i fit that, At £26 + postage it's not a lot and worth the try and I'll update you if it solves my problem.
If anyone else has an idea to try, I'm more than eager to hear.
After that, I have a contact in my local college who teaches Auto Mechanics, they'll have a look, but not sure how i feel if i have to let student repair it. But hey-ho everyone has to start somewhere.