The miqat for Umrah for those in Makkah is the area of al-Hill. When Aisha (may Allah be pleased with her) insisted that the Prophet (peace and blessings be upon him) perform Umrah alone after having performed Hajj with him in conjunction with it, he ordered her brother Abd al-Rahman to go with her to al-Tan'im so that she could enter ihram for Umrah from there. This was the closest area to al-Hill to Makkah, and this was at night. If entering ihram for Umrah from Makkah or from any other part of the Haram were permissible, the Prophet (peace and blessings be upon him) would not have made it difficult for himself, Aisha, or her brother by ordering her brother to go with her to al-Tan'im so that she could enter ihram for Umrah from there. This was at night, and they were on a journey and needed to wait for them. He would have permitted her to enter ihram from her home with him in the valley of Makkah, in accordance with the tolerance and ease of Islamic law. He was never given a choice between two matters except that which was easier, as long as it was not sinful. If it was sinful, he kept people away from it. He only permitted entering ihram for Umrah from the valley of Makkah. (A book of fatwas related to the rulings of Hajj, Umrah, and visitation by Sheikh Ibn Baz).
If a man in ihram, whether male or female, loses hair while wiping it during ablution or ritual washing, it does not harm them. Similarly, if a man's beard, mustache, or nails fall, it does not harm them if he does not do so intentionally. What is prohibited is intentionally cutting any of his hair or nails while in ihram. Similarly, a woman should not intentionally cut anything. As for unintentionally falling hair, these are dead hairs that fall out when moving, and their falling out does not harm them. (Fatawa Concerning the Rulings of Hajj, Umrah, and Visitation by Sheikh Ibn Baz)
If someone performs Hajj with a group and assumes ihram for Hajj individually, then travels with them for Ziyarat, it is recommended that he make his ihram an Umrah, perform tawaf for it, perform sa'i, and shorten his hair. He then exits ihram and enters ihram for Hajj at its proper time. He will thus be performing tamattu' (pleasure of the Hajj), and he must offer a hadiy (sacrifice) for tamattu', as the Prophet (peace and blessings be upon him) instructed his companions who did not have a hadiy (sacrifice) with them. (A book of Fatwas related to the rulings of Hajj, Umrah, and Ziyarat, by Sheikh Ibn Baz)