Two Different Whining Noises

[Alex.d.abbott]

I did a bit of searching for this, but couldn't find anything that seemed specific to my issue, so I am sorry if someone has covered this already.

The issue that I am having is twofold, though I suspect they are entirely unrelated other than maybe brought on by cold.

1.
On a cold start, especially when it is cold out, there is a whining noise right on engine start. It goes away after a second or two. The best way I can describe it is that it sounds kind of like Chewbacca. Recently, this has started coming on when I accelerate a little harder than just starting from a stop light, say to pass someone quick. It once again only makes the noise for a second or two, though it doesn't necessarily seem to be tied to the turbo spooling up.

2.
The other noise, which just started with the cold coming here in Cleveland is a very high pitched whine that seems to be independent of speed, acceleration, radio, braking, and A/C that is on whenever the car is on and sounds like it is emanating from the middle of the cabin. It is fairly quiet and can really only be heard with the radio down low or at the quiet part in a song.

Any help will be appreciated in pinpointing either of these issues, and let me know where I need to elaborate more in my descriptions.

[Alex.d.abbott]

After googling around some, it seems that the noise in the cabin that I mentioned could be the fuel pump. It was replaced this past January, but I have no idea how reliably as it was done by a general mechanic in Kansas who didn't specialize in German cars (emergency fix during a road trip). I am not sure the fuel filter has ever been replaced, so is it likely that that could be causing the issue with the pump whining?