What is required of me if I left the throwing of the Great Jamrah on the day of Eid, and the Middle and Small Jamrahs thereafter due to incapacity? And is it sufficient for the throwing to be done on my behalf without my consent, or by appointing someone who is not in a state of ihram? And is my Hajj valid, and what is required of me? And can what is required of me be performed at my residence or in Makkah?

Throwing the pebbles (ramy al-jimār) is obligatory. If one misses three pebbles or more, a damm (sacrifice) becomes incumbent upon them according to the majority of scholars. Your sister's son throwing on your behalf without your authorization does not fulfill the obligation. Throwing the three jimar on the days of Tashreeq can be delegated (by tawkeel) if you are unable to stone yourself, and it is not a condition for the agent to be in a state of ihram (definition). The place of slaughter is the Haram (definition), and the meat is distributed among the poor of the Haram.