Is offering hospitality with the right hand Sunnah, and after offering hospitality to the eldest, does one start with the person to his right and then the one next to him, or with the person to his left?

Taking and giving with the right hand is a recommended Sunnah, based on the Prophet's (peace and blessings be upon him) saying: "Let each of you eat with his right hand, drink with his right hand, take with his right hand, and give with his right hand, for indeed Satan eats with his left hand, drinks with his left hand, gives with his left hand, and takes with his left hand."

As for hospitality, the Sunnah is to begin with the person on the right, even if they are younger in age, due to the Prophet's (peace and blessings be upon him) action and his saying: "The ones on the right, the ones on the right; indeed, give to the right."