1). If the skin is oily and there is natural oil on skin , is it ok to do wuzu over it or is it necessary to wash it off oil each time with soap?
2). While in ehram, can we use towel to wipe face, considering the ruling that women don’t have to cover their faces

1) If it is oily then wash it because it stops water to reach.
2) Do not wipe yes it consider as covering of face.