Hey everyone :D

I'm a little bit confused about an issue I was having,
I have an Audi 2008 A3 2.0T with 107,000 km on the clock.
Two weeks ago I started having rough idle only on cold morning start ups. the rough idle disappeared after the temp gauge started to move a bit and that's it ,
RPM was normal, but when trying to rev up a little bit the rpm would go up and down (i have a video if that would help) .

I didn't have any check engine light but on one of those cold mornings, I had a fault code detected with OBDELEVEN =P0171 SYSTEM TO LEAN.
So I started diagnosing the issue from that.

the next morning i used OBDELEVEN to check misfire and it did a cycle of 130 misfires most of them came from Cylinder num 4 then 1, cylinder 2 and 3 were pretty ok.
after searching the web i came across PCV valve failure symptoms, i had most of them.

i checked the pcv by removing the oil cap and dipstick (not at the same time) when the engine was running .. i had a suction and a pop sound and the engine went really rough when i removed them ..
from what i saw on the web this is indicating a failure on the PCV ,i also could hear a small whistling noise on those cold starts coming from the little hole on the pcv itself which is also indicating a failure.
i ordered a PCV valve from amazon 06H-103-495-AH and replaced it with my pcv 06H-103-495-A that came out of the factory , and the next morning the issue disappeared! YAY!
just for the heck of it i checked the symptoms again and that's why i think something is strange.
now after the replacement when pulling the dipstick out the idle stays completely the same, correct me if im wrong but this means that the PCV is faulty, if I'm removing the oil cap the engine will go rough until i seal it back .
aside from that i get a better fuel mileage and the issue mentioned above with the misfires has been solved , another thing i noticed which im not sure if it was before is when im removing the oil cap , a white smoke comes out from there , is that normal ?

Thanks in advnace and sorry for the long post :D