Ruling on one who prayed behind an imam with an intention wavering between two prayers

The following message was received by the program from Riyadh, sent by one of the female listeners, saying: (N. H. S.) Our sister says: I performed the obligatory Hajj with my father when I was twenty years old, and during the tawaf or sa'y, the prayer was established, and I prayed with the imam while I did not know whether the time was for the midday prayer or the afternoon prayer; because I was distressed from fear and the large number of pilgrims.
Second: I performed the farewell tawaf while I was not in a state of ritual purity, and I know that the farewell tawaf is not waived for one in that state.
Answer: As for the prayer you prayed with the imam while you did not know what it was, whether it was the midday prayer or the afternoon prayer, you must repeat both the midday prayer and the afternoon prayer that you did not verify you performed on that day, with the intention for that day. You repeat the prayer for that day, the midday prayer and the afternoon prayer. As for the farewell tawaf that you performed while you were not in a state of purity, you owe a sacrificial animal; because you did not actually perform the tawaf. Tawaf without ablution is not lawful and does not suffice. So you must slaughter a sacrificial animal in Mecca for the poor. You entrust a trustworthy person from the people of Mecca or from those heading to it for 'Umrah or Hajj to slaughter it on your behalf with the intention for the farewell tawaf, and praise be to Allah.
As for what concerns Madinah, you owe nothing; because you made a mistake, but you do not have to make up anything. If you entered the Prophet's Mosque while you were not in a state of purity, you owe nothing. But if you prayed the obligatory prayer without purity, you must repeat it. As for merely entering the mosque without purity, you owe nothing for that. Yes.
The presenter: May Allah reward you. This modesty that many of our female listeners mention, perhaps His Eminence the Shaykh has a guidance regarding it?
The Shaykh: Yes, it is not permissible to be modest in such a matter. This modesty is not an excuse. And Allah does not shy away from the truth, Glorified and Exalted is He. So if a woman is not in a state of purity during the time of tawaf or the time of prayer, she says: I am not in a state of purity, just like a man. She goes to Zamzam or to another place to perform ablution for prayer, and she does not pray without purity and does not perform tawaf without purity. There is no modesty in this; it happens to everyone; the woman and the man, everyone experiences a state of ritual impurity, the man and the woman, the young and the old, even the prophets, when they experienced a state of ritual impurity, they performed ablution, and they are the noblest of people.
So the result is that there is no modesty in this, and Allah says: [Al-Ahzab:53].
So the point is: It is obligatory for the believer to speak the truth and not be modest, and likewise it is obligatory for the believing woman to speak the truth and not be modest in this, whether it is in the matter of ablution or the full ritual bath for major ritual impurity or otherwise. Yes.
The presenter: May Allah reward you.