Is a compensatory sacrifice (fidyah) of a sheep required of me for cutting my hair and exiting the state of ihram due to the onset of menstruation during Umrah on behalf of my deceased grandmother, and must it be sacrificed in Mecca or is it permissible in Egypt?

Menstruation does not invalidate 'Umrah; rather, it prevents circumambulation (Tawaf) according to the majority of scholars. If you have not completed your 'Umrah, you remain in the state of Ihrām, and you must refrain from the prohibitions of Ihrām and return to complete it (Tawaf, Sa'y, and Taqsīr). If you are unable to return, your ruling is that of one who is prevented (muḥṣar), so you would exit Ihrām by sacrificing an animal (hady) at the place where you were prevented (or by appointing someone to sacrifice it in Mecca). If you are unable to offer the hady, then fast for ten days. You are obligated to pay a fidyah for cutting your hair before exiting Ihrām, which is: fasting for three days, or feeding six needy persons, or sacrificing a sheep in Mecca.