The 4x4 system works via a viscous coupling between the front and rear axles, it's commonly referred to as torque on demand.
This coupling works automatically, it detects how much power is being transmitted and as torque on the rear prop shaft increases, the oil in the coupling heats and expands, causing plates to grip and lock together inside coupling so then it can transmit the torque through it to the rear axle.
The front and rear diffs are open diffs similar to most cars. (though some 4x4 models come with a "mock" diff lock called ELD that uses the ABS and traction control system to brake slipping wheels thus sending torque to the other wheel on that axle)
With a two wheel drive car, odd size wheels aren't a big issue as the open diff can allow the wheels on the driven axle to spin at different speeds, it needs to do this otherwise you'll never get around corners.
Trouble with these torque on demand systems is now the rear axle is connected.
An odd size wheel/tyre on an axle puts the coupling and the associated connecting shafts under strain.
Though the opens diffs can cope side to side, it can't cope to well front to back.
Off road when wheel grip is low, it's not too much of and issue if they all start slipping and sliding at different speeds, but on tarmac with grip on all corners, it can put too much strain back through the coupling and shafts.
Some cars have had real issues with this system, like the Merc GLC.
They seem so sensitive that one new tyre, which is ever so slightly larger than the other three slightly worn ones, causes the other three to hop and jump as they struggle to keep up with the larger one, damaging the drivechain, so Merc recommend you replace them in pairs.
As far as I can tell (I own one), the Panda 4x4 seems to be able to handle a single new tyre as long at it's the same size.
So you really need a spare wheel with the same circumference as your standard wheels.
They are available but you also need the extended jack as the 4x4 is higher up.
Fiat sell them, but they are cheaper here
https://www.thewheelshop.co.uk/
As I don't know what wheel/tyre size your car is, I can't pinpoint the actual spare wheel/tyre, but if you find your wheel/tyre size in your handbook, it should also tell you the size of the spare you need.
In regards to wheel balance, a wheel and tyre should be balanced whenever the tyre is fitted to the rim or if there are wheel vibrations (usually caused by losing a wheel weight) it should be rechecked.
Tyre fitters should do this as a matter of course when fitting on a machine, it only takes a few moments.