[CaseyFronczek]

As a Shafi'i, I am taught that qunut is only to be recited during fajr prayer only (sunnah muakkad).
Never been taught that it can also be recited in other prayers.

And regarding to qunut nazilah, is it a sunnah?

Stick to doing it in the Fajr prayer, this is the Sunnah.
As for Qunut Nazilah, this is done when the Ummah are struck with calamities and such, not always. However, some argue that because of the state of the Ummah today, one can perfom it regularly.

Allahu a'lam