If you're not a believer, assume for the sake of answering the questions that God exists and that he's good.
I'm not sure what the difference would be between 1-2 and 3-4 given the above, but I'm assuming in the first instance we are saying there is no doubt that God commanded it while in the second there is.
But if I assume there is a God and "he is good", and I'll add in s/he/its also omnipotent, omnibenevolent, and omniscient, then the answer should be yes to 1-2, and no to 3-4 on the grounds that I am intepreting 3-4 as leaving the door open for the person being wrong even if God is real with the qualities outlined above. Given the consequences of being wrong, it only seems reasonable a person needs to have more than sincere belief. Yet, I can't square my own thinking with the proposition that a God who would command this is also good.
(1) If God commands you to kill your own child, then you should do it.
(2) If God commands somebody to kill their own child, then they should do it.
(3) If you sincerely believe that God has commanded you to kill your own child, then you should do it.
(4) If somebody sincerely believes that God has commanded them to kill their own child, then they should do it.