Did it work OK when they bridged the relay?
If so, could be just the relay is faulty, or the connections inside that box have failed.
You can DIY repair the box internals as shown here:http://www.fiatcoupe.fr/entretien-Boitier-Clim.php
but probably easier to just replace it with a good used one. Also worth cleaning the relay pins and the socket in the box with a thin file.
As for the internal fan, could be the climate ECU if the rear screen heater is working manually but not from MAX DEF setting. But double check the fuse and holder in engine bay (exposed 30A) and the wipers fuse in main fuse box, I think the climate ECU also takes power on that circuit.