Is it necessary to bid farewell to all loved ones and relatives when going for Hajj, or is it sufficient to bid farewell to the closest ones?

There is no obligation to bid farewell to family and relatives when going for Hajj. Rather, it is recommended for a Muslim to bid farewell to his Muslim brother upon any journey. The Prophet, peace and blessings be upon him, and his Companions used to bid farewell to each other by saying: "I entrust to Allah your religion, your trust, and the consequences of your deeds," as mentioned in the hadith (definition) of Ibn Umar. This indicates that bidding farewell is recommended, not obligatory, and there is no difference between Hajj and other journeys.