Is it obligatory for someone coming from Ta'if for Umrah to enter into a state of ihram from the miqat of As-Sail Al-Kabeer, or from their home? And is it permissible to enter into a state of ihram from the family home in Makkah that is located outside the Haram boundary?

As long as you are from Ta'if and will pass the miqat with the intention of performing the ritual, you must enter into ihram from the miqat of Qarn al-Manazil ("As-Sail al-Kabeer"). This is because it is the miqat for the people of Ta'if and those in their vicinity, and due to the generality of the Prophet's (peace and blessings be upon him) statement concerning the miqats: "They are for them and for those who come upon them from other than them, among those who intend Hajj and Umrah."