A) Temp sensor provides input for climate air conditioning (not manual), otherwise it simply gives you ice warnings and, obviously, a reading of the outside temperature.. To the best of my knowledge, the sensor can not be purchased separately; you might need to get the whole mirror assembly (this will not be cheap). If replacement is not an option, you could try to clean the sensor and check the wiring and plug (i.e. higher resistance due to a corroded connection would definitely cause the reading to be off). Use search for further information regarding sensor location and removal (fortunately I’ve not had to do this yet.. thus I cannot give you any further instructions).
B) Parking system clearly has a sensor, wiring, or some other failure.. Use search for more detailed instructions but I will give you some tips and possible solutions below:
1) Plugs and wiring:
1.1) Main sensor plug:
This has a history of getting damp/dirt in it and thus no signal gets from the sensors to the control unit.. The plug is located in the lower part of the bumper (right side if you are facing the rear) and can be reached through an access hole in the lower section of the bumper.. Try unplugging it and spraying contact cleaner on the contacts and plugging it in/out a few times.. If that solves it... spray some WD40 on the plug to keep the moisture out (at least temporarily) and tuck it into a section of the bumper that would keep it dry and away from the access hole (i.e. dirt/water normally gets in when the plug, which is free to move, gets near the access whole) you could also try wrapping it securely with cling film and tape (but ensure water cannot get in i.e. use WD40 on the inner layers).
1.2) Control unit and plugs:
Assuming you have managed to get you boot damp (i.e. due to water being spilled or a leak via the tailgate (i.e. the fog lights.. and yes you would be hard pressed to notice it) the moisture could have corroded the control unit connections and/or the unit itself. You could try contact cleaner on the plugs as advised in 1.1 (but the unit cannot be diagnosed without special equipment.. this I wall explain below at some point). Likewise the control unit is located on the right side of the car (if you are facing the boot). Open the little access panel (as you would to change a bulb in the tail light) and you would find a little black box mounted to the body of the car under (though a bit to the right really) the tail light.. You can’t miss it.. Have a poke about.. It would have 2 cables running through it. This also gets you to a temporary solution.. If you unplug these cables you would, effectively, disconnect the unit.. Although this would still give you a warning message every time you start the car (and would show a warning triangle on the dash at all times) it would stop buzzing when you are reversing (the good news is.. because you get buzzing the control unit is still able to send out a signal.. thus the chances are it is operating).
2) Sensor failure (there are 4). There could be many reasons for these to fail but the two primary causes are physical damage (i.e. due to impact) and dirt..
2.1) How dirt can cause sensor failure:
The sensors have 2 breathing holes to let moisture out.. Unfortunately, a power washer can drive dirt into the sensors via these holes causing them to malfunction. You could try to remove the sensor/s and, using a compressed air canister, try to blow the dirt out via the breathing holes (you could also try to wash the dirt out.. but let the sensors dry for 24 hours before you put them back into the car.. and be aware that the likelihood of failure is high.. as these sensors were not designed to function in an aquatic environment.. it’s a car not a sub

).
2.2) Physical damage or failure:
As you could have guessed (and why not?!) the sensors cannot be taken apart and checked/cleaned, thus if one or more have failed (either due to 2.1 or any other cause) it has to be replaced (do ensure that there is power i.e. the failure is not due to plugs/connections). There is a very easy quick way to find a dead sensor (note that a sensor clogged with dirt would not be detected this way.. although going back to dirt.. taping the sensor might move/dislodge the dirt a bit and the system might start working again, although only temporarily). So how can you detect a (completely) dead sensor? Well (with engine off as you don’t want to smash into the car/cat/wall/mother in law behind you) put the key to mil position (to power on all the electrical systems) and put it in reverse gear (do ensure that the hand brake is on and that some one is in the vehicle to stop passers by getting in and driving off while you are crouching behind the vehicle.. trust me on this one.. it may look fine while you are crouching with the car there.. but if it were to drive off while you are still couching.. it would look a bit odd..). Once you have managed the above, walk to the rear of the car and bend down (sticking you bum out is optional.. only do so if you’re a girl) now put your ear to each sensor in turn.. If the sensor is powered on you would hear clicks (kind of like a sonar) at regular intervals.. if you find one that doesn’t click.. that’s you problem. If none click, then either you can not hear well at that frequency or the problem is with the wiring or control unit.
3) Controller failure:
This is a smart node and if the above fails this is the likely cause.. How can you fix this problem?! Replace the controller (you don’t want to know how much it would cost). Can you find out what the problem is specifically? Yes you can.. take it to your nearest fiat authorized (or otherwise) garage that has a fiat diagnoster.. as this would have the ability to interface with all your smart nodes and it would also be able to tell you what sort of a fault you have (it can even tell you which sensor has failed

)
Other things to note:
a) Unlike aftermarket systems, fiat controller would not work without all 4 sensors present and functioning (so no.. you cannot find a faulty sensor by unplugging them one at a time..)
b) Sensors are quite cheap.. about £35
c) Diagnostics should also be about £35
d) Controllers are best obtained second hand
e) Sensors are best obtained new (as second hand would likely have the same problem i.e. damage, dirt, etc.)
f) Hope you not sorry you’ve asked… and that you’ve managed to read this through to the end (understanding is a different issue all together..)