Praise be to Allah.

Firstly:

The scholars differed concerning the ruling on doing ‘umrah repeatedly during a single journey. The correct view is that it is not prescribed, and it is not permissible to do ‘umrah more than once in a single journey. If a person enters Makkah to do ‘umrah, it is not prescribed for him to repeat it, either on his own behalf or on behalf of anyone else, unless he leaves Makkah without intending to come back to it to do ‘umrah. Then it is permissible for him, if he enters Makkah again, to do ‘umrah on his own behalf or on behalf of someone among his relatives or family who did not do ‘umrah. What many people do nowadays of repeating ‘umrah many times in one trip is not in accordance with the practice of the Prophet (blessings and peace of Allah be upon him) or that of his companions (may Allah be pleased with them), and they are the ones who used to strive hard to reach Makkah al-Mukarramah and were filled with longing to do ‘umrah, because of the great reward it brings.

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:

Abu Taalib said: I said to Ahmad: Tawoos said: As for those who entger ihram for ‘umrah from at-Tan‘eem, I do not know whether they will be rewarded or punished. It was said to him: Why would they be punished? He said: Because they have forsaken circumambulation (tawaaf) around the Ka‘bah and gone out a distance of four miles, and in the time it takes to come from four miles away he could have done two hundred circuits of tawaaf, and the more one does tawaaf the better it is than walking for no reason.

Ahmad approved of these words of Tawoos, which Abu Taalib asked him to testify to. This was narrated by Abu Bakr in ash-Shaafi.

Majmoo‘ al-Fataawa (26/265)

And he (may Allah have mercy on him) said:

For example, if a person whose house is close to the Haram does ‘umrah every day, or every two days, or the one who lives close to the miqaat that lies between him and Makkah does ‘umrah every day or every two days, or five times in a month, or six times, and the like, or one who begins his ‘umrah from Makkah does ‘umrah once or twice every day, this is makrooh according to the consensus of the early generations of this ummah. None of the early generations did that; rather they were unanimously agreed that it is makrooh, even though a group of fuqaha’ among the companions of ash-Shaafa‘i and Ahmad regarded it as mustahabb. They have no proof for that at all, except general analogy, which is that this is doing a lot of acts of worship, or clinging to general notions about the virtue of ‘umrah and the like.

Majmoo‘ al-Fataawa (26/270)

Ibn al-Qayyim (may Allah have mercy on him) said:

There is no case in which the Prophet (blessings and peace of Allah be upon him) did ‘umrah starting out from Makkah, as many people nowadays do. Rather in each of his ‘umrahs he entered ihram for ‘umrah when he was heading towards Makkah. After the revelation began, he remained in Makkah for thirteen years, but there is no report to suggest that he did ‘umrah at all during this period starting out from Makkah. The ‘umrah that the Messenger of Allah (blessings and peace of Allah be upon him) did and prescribed was the ‘umrah of one who comes into Makkah (from outside the city), not the ‘umrah of one who is in the city and goes outside of the Haram boundary in order to do ‘umrah. No one ever did that during his time, except ‘Aa’ishah alone, out of all of those who were with him, because she had entered ihram for ‘umrah, then her menses came, so he instructed her to incorporate ‘umrah into Hajj, so she changed her intention to qiraan [Hajj and ‘umrah together], and he told her that her circumambulation of the Ka‘bah and her going between as-Safa and al-Marwah would count for both her Hajj and her ‘umrah. But she felt upset that her co-wives would be going back having done Hajj and ‘umrah separately, because they had done tamattu‘ and had not gotten their menses, and they had not done qiraan, but she would being going back having combined her ‘umrah with her Hajj. So the Prophet (blessings and peace of Allah be upon him) instructed her brother to take her to at-Tan‘eem to enter ihram for ‘umrah, so as to console her. But he himself did not do ‘umrah from at-Tan‘eem during that pilgrimage, and neither did anyone else among the people who were with him.

Zaad al-Ma‘aad (2/890, 90)

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) was asked:

What is the specific period after which one can do ‘umrah? If a person comes after a week, for example and he did ‘umrah one week before, can he do ‘umrah now?

He replied:

Imam Ahmad (may Allah have mercy on him) mentioned an approximate limit. He (may Allah have mercy on him) said: If his head has turned black (i.e., his hair has regrown) after shaving it, then he may do ‘umrah, because in ‘umrah it is essential either to cut the hair or shave the head, and that cannot be done until after the hair has grown back. As for what some people do nowadays in Ramadan, or during the days of Hajj, where they do ‘umrah every day, this is an innovation (bid‘ah), and they are closer to earning a burden of sin rather than attaining reward. Therefore the seekers of knowledge must explain to these people that this is something that has been newly introduced, and it is an innovation. They cannot be more keen (to do good) than the Messenger (blessings and peace of Allah be upon him) or the Sahaabah, but the Messenger of Allah (blessings and peace of Allah be upon him) remained in Makkah for nineteen days during the conquest, and he never thought of going out and doing ‘umrah. Similarly, during ‘umrat al-qada’ he did ‘umrah and remained there for three days, and he did not do ‘umrah a second time. Likewise the Sahaabah (may Allah be pleased with them) did not do ‘umrah repeatedly.

Liqaa’aat al-Baab al-Maftooh (72/question no. 20)

For more information on the difference of scholarly opinion concerning the ruling on doing ‘umrah several times in one year, please see the answer to question no. 109321

Secondly:

The basic principle concerning a woman who gets her menses is that she is not allowed to circumambulate the Ka‘bah. If she has done tawaaf al-ifaadah, then she may leave, and the farewell tawaaf is waived in her case. If she has not yet done tawaaf al-ifaadah, then she must wait until her period ends and she becomes pure, then she should circumambulate the Ka‘bah. The fact that she is with a group is not an excuse for her to omit tawaaf, or to do tawaaf whilst she is menstruating, if they can wait for her, or she can delay leaving Makkah in the company of her guardian.

It is important to differentiate between the one who is able to go back to Makkah and do that tawaaf, and the one who cannot do that except with great hardship. If a woman’s home is near Makkah, or she will be able to return to Makkah to do what she still owes of tawaaf al-ifaadah, then she can leave with her group – if she is not able to stay in Makkah – so long as she will return to do that  tawaaf, and on condition that her husband – if she is married – will not be intimate with her, because she has not yet completed the second stage of exiting ihram. Then she should come back to Makkah and do tawaaf al-ifaadah, and thus complete her Hajj.

In the case of one who cannot remain in Makkah or come back to it except with a great deal of hardship, it is permissible for her to do tawaaf as she is (i.e., menstruating). So she should do ghusl, wrap herself with something that will prevent blood from leaking, and then do tawaaf al-ifaadah.

Please see the answer to question no. 14217

Please see the answer to question no. 20465 concerning menses of a woman during ‘umrah.

And Allah knows best.