What should a girl do who does not remember whether her menstruation began before the time for prayer, or during it? And does she have to make up (the prayer/fast) if her menstruation began after the intention to break the fast and pray, and she does not know whether the menstruation came upon her before the time or after it?

Scholars differ concerning a menstruating woman making up prayers if menstruation began after the time for prayer had started. It is more prudent for you to make up the Dhuhr prayer for which menstruation began after its time had started, to avoid disagreement. If menstruation began and you do not know whether it was before or after the time for prayer, consider it to be after the time, because "the principle for every new event is to estimate it at the nearest time." Sheikh Ibn Uthaymeen was asked about a woman who saw menstrual blood after the Adhan but did not know whether it was before or after it. He replied that the default is that it had not yet started, and she must make up the prayer when she becomes pure, unless she saw the blood immediately after the Adhan, in which case it is likely before the time, and thus the prayer is not obligatory upon her.