With a Resurrection stone, the people who come from dead, speak according to the person who called them?

Question

Will the people who appear back from death speak the words which the User wanted to hear or, is that actually what the person would say?

Answer 1

I can think of a few things as proof that the shadows generated by the Stone really are dead:

1.The second Peverell's girlfriend In the story of the Three Brothers, the second brother asks for the resurrection stone to bring back the girl he was going to marry. Here is the text as Hermione read it in Book 7:

Meanwhile, the second brother journeyed to his own home, where he lived alone. Here he took out the stone that had the power to recall the dead, and turned it thrice in his hand. To his amazement and his delight, the figure of the girl he had once hoped to marry, before her untimely death, appeared at once before him.

Yet she was sad and cold, separated from him as by a veil. Though she had returned to the mortal world, she did not truly belong there and suffered.

I know it's not that much to go on since it's a children's story, but it's something.

2.What Sirius says in the forest.

"Does it hurt?"

The childish question had fallen from Harry's lips before he could stop it.

"Dying? Not at all," said Sirius. "Quicker and easier than falling asleep."

The fact that Sirius knew how dying felt proves that he had done it before. Although he would probably say this also if it were what Harry wanted. And so we move to the next one...

3.What Lupin says right after that.

"And he will want it to be quick. He wants it over," said Lupin.

This is definitely not what Harry wants to hear--that his death is coming up quickly, and there's nothing he can do to stop it.

4.The Appearance of Sirius and Lupin

Sirius was tall and handsome, and younger by far than Harry had seen him in life. He loped with an easy grace, his hands in his pockets and a grin on his face.

Lupin was younger too, and much less shabby, and his hair was thicker and darker. He looked happy to be back in this familiar place, scene of so many adolescent wanderings.

The fact that Lupin and Sirius looked so much younger than Harry had ever seen them, combined with their few helpful lines, is proof that Harry did not dream them up, they were truly brought back with the Resurrection Stone.

Answer 2

The shades are real

The shades called up by the Resurrection Stone do not converse much with Harry. There is little that they say that the Stone could not simply be drawing from his own memories of them. There is one thing, however:

“You’ll stay with me?”

“Until the very end,” said James

“They won’t be able to see you?” asked Harry.

“We are part of you,” said Sirius. “Invisible to anyone else.”

—Harry Potter and the Deathly Hallows

And lo and behold, later:

Two figures emerged from behind a nearby tree; Their wands flared and Harry saw Yaxley and Dolohov peering into the darkness, directly at the place Harry, his mother and father and Sirius and Lupin stood. Apparently they could not see anything.

—Harry Potter and the Deathly Hallows

The shade of Sirius gave Harry accurate (and counterintuitive) information about the functioning of the Stone that he simply had not known before: that the shades were invisible to everyone else. That strongly suggests that the shade had access to information that Harry did not, which in turn suggests that he is in fact literally the spirit of Sirius.

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For an additional piece of evidence, we can consult Goblet of Fire.

Harry experienced something quite similar in that book. When Harry's wand and Voldemort's connected, they experienced Priori Incantatem, and echoes of those Voldemort had killed came from the wand. When James Potter emerged, he gave Harry some advice:

And he came...first his head, then his body...tall and untidy-haired like Harry, the smoky, shadowy form of James Potter blossomed from the end of Voldemort’s wand, fell to the ground, and straightened like his wife. He walked close to Harry, looking down at him, and he spoke in the same distant, echoing voice as the others, but quietly, so that Voldemort, his face now livid with fear as his victims prowled around him, could not hear....

“When the connection is broken, we will linger for only moments... but we will give you time...you must get to the Portkey, it will return you to Hogwarts...do you understand, Harry?”

—Harry Potter and the Goblet of Fire

Clearly this shade was an entity independent of Harry's consciousness, since it told Harry two things he did not know:

1. The Portkey would take him back to Hogwarts. Nowhere in the instructions given to Harry before the third task did it say this.
2. When the connection was broken, they would linger only a few moments. This was true, as demonstrated soon thereafter. Harry, of course, had no idea how Priori Incantatem worked.

This is from an entirely different situation. Why is it relevant?

This shows that a well-known effect can produce shades of the dead with independent knowledge and consciousness. Like the Resurrection Stone, of course, it does not truly bring the dead back to life, but it brings forth an echo of their consciousness. In other words, it is obviously possible for an effect very like that of the Resurrection Stone to be reproduced. There's no good reason to suppose that the second Peverell brother was not able to "bottle" this effect and store it in the Resurrection Stone.