Is the resident pilgrim in Mecca obligated to perform the Arrival, Farewell, and Ifadah circumambulations, and when should the Farewell circumambulation be performed if he wishes to delay it, and is it permissible to perform Umrah before the Farewell circumambulation if the pilgrim remains in Mecca after the Hajj?

Tawaf al-Qudum (circumambulation of arrival) is a Sunnah (recommended act), and the Tawaf you performed upon your arrival in Mecca for 'Umrah suffices for it. Tawaf al-Ifadah (circumambulation of overflowing) is a pillar (Rukn) by scholarly consensus. Its time begins from the middle of the night of 'Eid al-Adha (the Day of Sacrifice), and there is no specified end time for it according to the majority of scholars. A pilgrim does not complete the major disengagement (at-Tahallul al-Akbar) from the state of ihram except by performing it. Tawaf al-Wada' (farewell circumambulation) is obligatory for anyone wishing to depart Mecca, and the proof for this is the Prophet's (peace be upon him) command: "No one should depart until the last thing he does is circumambulate the House." This is lenient for a menstruating woman. If you wish to perform 'Umrah after Hajj while residing in Mecca, go out to the nearest point outside the Haram boundary (adnal-hill) and enter the state of ihram from there. If you wish to leave Mecca, perform the farewell Tawaf immediately before your departure, and do not engage in anything after it except travel; otherwise, you would be required to repeat it.