If there is ritual impurity (najasa) on part of the face, does this necessitate washing the entire head for someone with oily skin, and must the eyebrows be washed due to the possibility of them being impure?

If you find impurity on a part of the face, you must pour water only on the spot of the impurity until it is removed. There is no need to wash the rest of the face or head, whether the skin is oily or not.

As for what is doubted to be impure, the default is that it is pure, and it is not obligatory to wash it merely due to doubt. Rather, only that which is certainly impure should be washed.

It is obligatory to resist whisperings (waswas) and strive to get rid of them, because succumbing to them leads to great evil.