Can someone go to Haj on behalf of a person who has passed way? if yes; what should the characeristics of the person going on behalf of the person passed away be? Thank You
Yes, you can do on behalf. It is called Hajj-e-Badal in URDU.
Sayyidina Abdullah ibn Buraydah (RA) reported from his father that a woman came to the Prophet (SAW) and said, "My mother has died and did not perform Hajj. May I perform Hajj on her behalf?" He said, "Yes, you may perform Hajj for her."
[Muslim 157, Abu Dawud 2877]
You can also Sacrifice on behalf of dead.
Sayyidina Ali (RA) always sacrificed two rams, one on behalf of the Prophet (SAW) and one on his own account. Someone asked him, Why do you do that? He said, 'The Prophet (SAW) had commanded me to do it. So I will never neglect it."
[Abu Dawud 2790]
You can pay Saddaqah on behalf on dead.
Sayyidina Ibn Abbas (RA) reported that a man submitted, "0 Messenger of Allah! My mother has died. Will it benefit her if I give sadaqah on her behalf? He said, 'Yes. The man said, "I have a garden and ask you to witness that I have given it as sadaqah on her behalf".
[Bukhari 6771 Abu Dawud 2882, Nisai 3656]
And a list I have provided you here already.