The vehicle has obviously been operating in a dusty enviroment, and the cover from the engine bay fusebox is missing. Dust can cause electrical problems. Given the symptoms reported, and that this fusebox is a common point, it would be sensible to either strip and thoroughly clean the fusebox, or alternatively replace it. Used boxes are available on Ebay, but do check the part number if purchasing. Cleaning a similar fusebox is described here.
The cover isn't missing, I just removed it so that I could get a good view of everything and also inspect the part of the loom where it enters the fusebox. Although you are correct about it being extremely dusty here in Israel. Potentially taking that fusebox apart and cleaning it is on my todo list, but I think I'm leaning right now more towards that "ignition switch contact holder block" problem mentioned in the Fiat Recall. I'm assuming that the "block" mentioned there is the "B" connector on the B002 JUNCTION UNIT UNDER DASHBOARD listed in eLearn. I assume that because I see that the pins on that connector go to the ignition switch, radio, air bag, body computer, and instrument panel. Unfortunately I can't see the function of those pins, only their origin, destination and color of wires... That junction box just seems like a potential common point of failure for all the varied problems I'm having and the fact that there was a Fiat recall with similar symptoms even though the recall doesn't cover my specific vehicle seems to my like it might still be the problem.
Not sure what to do about it... Just try and get another junction unit from a junkyard or off ebay and replace it and see if that helps? Maybe just unplug and replug all the connections on the junction box?