Why is the right hand predominantly used in most matters, and why do Arabs consider it a good omen, and why is the right shoulder uncovered during Hajj, and why is the right hand used for shaking hands and eating while the left hand is restricted to washing and similar activities?

It is Sunnah to use the right hand for all matters of honor, such as ablution (wudu'), ritual bathing (ghusl), dressing, entering the mosque, eating and drinking, and touching the Black Stone. The left hand is used for removing impurities. Similarly, baring the right shoulder during circumambulation (idtiba') is a Sunnah, and it is recommended to do so in imitation of the Prophet, peace and blessings be upon him.