A couple of things -
I really think it's worth doing the tyre swap before you spend any more time and money on it, as detailed in post 4 above.
Tyres damaged by hitting kerbs can look OK but deform when rolling, giving funny noises and vibrations.
Also, I need to be sure we're talking about the same parts, as in UK speak the Panda has a steering rack (rack and pinion, rather than a steering box, which I understand to be old technology - a worm gear and recirculating ball - and a bit wooly by comparison, but doesn't kick back on rough ground).
Here's a picture of the bits I think we're talking about on the Panda:
there you can get play in:
the ball joint known as "track rod end" - you can see the play in that joint when the road wheel is moved as if to turn the car left then right, or when the steering wheel is moved to left then right etc.
the ball joint inside the bellows at the end of the rack can also wear, but you may need to squeeze the bellows to feel the joint, while somebody else pushes and pulls at the road wheel, or steering wheel - you'll feel if it is worn. The one off the dismantled CL was still so tight you could position the arms to any angle and they wouldn't move under their own weight, even with the track rod end joint on the end of the arm.
with some steering lock on for a right turn, get hold of the bellows and see if you can move the rack about - check up/down, and fore/aft, a bit of movement there may give you a noise described as "clatter" when traversing bumpy ground. I suppose if it was badly worn you'd feel that through the steering.
The thing is though - these items are checked as part of the annual vehicle test (MOT in UK), so you'd find out soon enough if there was a problem here, but I don't know how severe tests are in Italy.
Post back to let us know if I'm in the right area..