Is it permissible for the wording of the Istikhara prayer to be a request for her fiancé to divorce her if that is good, or to ask to leave him if that is good, and when is it performed, and how is its result known?

It is not clear whether what happened was a valid marriage contract (aqd shar'i) or merely an engagement (khitbah). If it was merely an engagement, then each party is free to annul it whenever they wish. Obedience to the mother in annulling the engagement is not obligatory unless there is a legitimate reason (masuwagh shar'i). In this case, there is no need for Istikhara (guidance prayer) concerning an obligation. If there is no legitimate reason, then Istikhara is permissible. However, if a valid marriage contract was concluded, then you have become a wife, and it is not permissible for you to seek divorce except for a legitimate excuse. In that case, Istikhara becomes legislated, and its supplication should include naming the specific need. It can be performed at any time except during times when prayer is disliked. If seeking divorce is not permissible, then there is no Istikhara concerning it.