The whir at the rear is the cambiocorsa pump priming the hydraulic system. I'm not sure what else would click loud enough that you would hear it in the cabin, except for maybe the fuel door release, but that would be pretty odd. Is it only when you are starting the car, or perhaps going from neutral to first?
Maybe just some more details about when you hear it?
Hummmm... is it on the back left side (wheel) ? My car is due on the 14th to inspect exactly that sort of noise (clank-clank type) which has mystified the dealer some weeks ago when the car went-in for clutch replacement.
I told them: "there is some noise coming from the back"
Dealer: "we did a test-run and think comes from the front"
My reply: "fair enough"
After 2 weeks: "we checked on the front, went again for a test run, you're right, noise comes from the back... maybe a rubber suspension bush in need for replacement..."
My reply: WTF..?
So there we go.
In addition, the clutch seems not OK. It chokes on 1st gear (you just floor it, takes a DEEP breath, then goes... with the previous clutch it was a slam in the face as soon as you applied gas) and sometimes when down-gearing it just takes ages (slips) until engaging... this is particularly noticeable in hill-climbing.
I paid a little more attention to the sound, and actually what I'm hearing is a series (always the same) of electromechanical whines (kind of like what the seat makes when you're adjusting it) which goes on for like 3 seconds as soon as I open the door. And no, its not the window opening or the seat moving, as far as I can tell.
F Yu. The cambiocorsa pump is the hydraulic pump for the transmission. The cambiocorsa system that does the shifting for you uses hydraulics to do the same physical manuevers otherwise done with a manual shifter in a car, either by cables or direct rods. The electrohydraulic system needs power and pressure before the car can start, otherwise it can't get to neutral.