This article says that a Bishop allowed a Nun to marry a couple. Does the Bishop have the authority to do this? Or is this an abuse?
It sounds as though the bishop acted under the authority of the Code of Canon Law (1112 §1) which makes provision when certain conditions exist for lay persons (that includes women) to assist at weddings:
Where there is a lack of priests and deacons, the diocesan bishop can delegate lay persons to assist at marriages, with the previous favorable vote of the conference of bishops and after he has obtained the permission of the Holy See.