Is it permissible to travel from Egypt to the borders of Mecca without ihram, then enter into ihram from the miqat near Mecca three days later to perform 'Umrah, or is it obligatory to enter into ihram from Egypt and perform 'Umrah on the same day of arrival?

One must enter into a state of ihram from the miqat of the people of Egypt (Al-Juhfah or its equivalent parallel) for whoever intends to perform Umrah. It is not permissible to enter Makkah without ihram, and ihram from outside the Haram boundary (adna al-hill) is not sufficient. It is permissible to delay performing Umrah after entering ihram, provided one remains in the ihram garments and refrains from its prohibitions. However, performing it promptly is better for quick release from ihram and to avoid its prohibitions.