Is it obligatory for a woman in ihram to perform tawaf and sa'i for Umrah accompanied by her mahram, or is it permissible for her to perform tawaf and sa'i by herself?

It is not a condition for the validity of a woman's 'Umrah circumambulation (Tawaf) and striving (Sa'y) that her mahram be constantly with her during the Tawaf and Sa'y. Rather, she may perform Tawaf and Sa'y by herself, and her 'Umrah will be valid.