The face is the front of an animal's head that features three of the head's sense organs, the eyes, nose, and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities affects the psyche adversely.
Most of our Maraaji' of Taqleed state that covering the face of the female is not obligatory except when not covering the face can cause harm, but in usual cases, it is obligatory to cover all the hair, head, neck and whole body except the face and the hands.
There are certain narrations that say whenever you place out your hands and supplicate to Almighty God, when you finish you should wipe your face and head with your hands.
I have come across a tradition that says the reason for this is because angels receive the dua from your palms.
However, when it comes to Qunut, in your daily Wajib prayers, some Fuqaha deem it as makruh, and therefore it is best not to wife your face with your hands after Qunut, in faridhah prayers.
There is a recommendation for you to do this in Nafilah prayers.
Please refer to the view of your Marja' taqleed.
And Allah knows best.
Yes it is allowed as far as it does not amount to exposing her beauty in front of outsider man. Just removing unwanted hair from her face is allowed.
You do not need to cover your face for Hijab if the silver stud is not considered by common people in your society as an ornament.
You don't need to remove it during Ehraam unless it is understood as an ornament.