What is the ruling on delaying the Farewell Tawaf due to severe crowding, the distant location of residence, and studying outside the Haram boundaries, and then performing it afterwards?

Your brother's circumambulation (Tawaf) is valid. The disagreement is only regarding the necessity of a sacrifice (dam) for delaying it beyond the days of Tashreeq. The fatwa issued by us is that no sacrifice is due upon him. Delaying the Tawaf beyond the days of Tashreeq is disliked (makrooh), and this dislike intensifies upon departing Mecca before performing it.