She says, if a woman does not see purity except an hour or two after fajr, so she performs ghusl and fasts, what is the ruling on her fasting that day?

As for the woman upon whom the day begins while she is menstruating, her fasting is invalid. She is not allowed to fast or to abstain.

The Prophet ﷺ forbade that, as is reported in the two Sahihs in the hadith of Aisha, may Allah be pleased with her. So her fasting in that case is forbidden, and her fasting is an innovation.

As for the woman who is unsure: was her purity before fajr or after it? She is uncertain.

For example, the bleeding stops before fajr, but she does not see the white discharge except after fajr. What is her situation in this case?

We say, as long as she does not see blood, as long as she does not see blood during the day, then she is pure. As long as she does not see blood, then she is pure, and that is the white discharge.

It is not purity itself, but rather a sign of purity. That is, it is not purity in itself, but it is a sign of purity. So in this case, we say that she should fast.

And there is nothing upon her as long as no blood comes out, even for a moment during the day.

In that case, it is not allowed, and she must make up that day. There is no disagreement among the scholars about this. May Allah reward you, Shaykh. Abu Ziyad also via Twitter.