Is what the wife did, by inserting things into the anus of a strange man, considered a sexual abomination (fahisha of zina)? Does she have rights after divorce? Is it permissible to take her back after her repentance?

What the wife did is a reprehensible disobedience and a grave sin, but it is not fornication that necessitates the ḥadd punishment. Even if she were to commit fornication, her mahr (dowry) would not be forfeited because of it. Therefore, as long as you divorced her without stipulating compensation, she is entitled to all the rights of a divorced woman. If she repents, it is permissible to take her back.