Praise be to Allaah.
If a woman gets her menses, then the basic principle is that this menses remains until she is certain that it has ended, and it is not permissible for her to fast or pray when she is not sure as to whether her menses has ended or not.
‘Aa’ishah (may Allah be pleased with her) used to tell women to take their time and not to be hasty until they were certain that they had become pure. She used to say: Do not be hasty until you see the white discharge, meaning purity from menses.
Based on that, you do not have to make up Fajr prayer; as for Zuhr prayer you have to offer it because the time for it came when you were pure from menses.
As for the fast, the fast of that day is not valid -- if you fasted it -- because you were menstruating at the beginning of the day, and you have to make it up after the end of Ramadan.
And Allah knows best.