Are the 'Umrah and the prayer invalid due to the discharge of light and dark brown secretions after ghusl from menstruation?

Purity is achieved by the white discharge or dryness. Any brownish or yellowish discharge seen by a woman after achieving purity is not considered anything, based on the words of Umm Atiyyah (may Allah be pleased with her): "We did not consider the brownish or yellowish discharge after purity to be anything." Therefore, the brownish discharge you saw is not menstruation, and your 'Umrah is valid, unless the bleeding was continuous. If the continuous bleeding was menstruation, then your tawaf for 'Umrah is invalid, and you must remain in your state of ihram and return to Makkah to perform tawaf and sa'y, or exit ihram by offering a sacrifice for being prevented if returning is not possible. Some scholars consider the tawaf of a menstruating woman valid with a sacrifice, and it is permissible to adopt this view in case of necessity.