If you dont have the master key, you cant program new keys to the system.
Cant you just cut new key to the old lock and move the transponder to the cut key?
If you lost the key part, but still got the transponder, you could get the ignitionbarrel and keys form another and transplant the transponder to "new" key.
If all is lost, you need the stuff in your post, not sure about the reader on the lock, but it should be connected to the immobilizer so it comes with it? ECU and immobilizer are paired.
Getting keys coded for the car from fiat might be more expensive than scrappy parts....? I did read somewhere that you dont even get the code card in UK (code to bypass immobilizer with accelerator pedal presses).