Did Harry's Resurrection Stone family know he would survive?

Question

This question assumes that the shades Harry saw in the Forbidden Forest were really part of the souls of his parents, Lupin and Sirius and that they could think for themselves - which I believe is the point intended and a concensus reached on this site via other questions. (Practical value of the Resurrection Stone and Why didn't the resurrection stone 'work'? for example).

Assuming this is true, is there any evidence to clairify if they believed that they were genuinely supporting Harry in his approach to death or if they were somehow aware of Dumbledore's big picture?

What I mean is, could they share a secret comfort that all would be well, or at that moment did they believe they were shepherding their son/close friend to be murdered by an evil, frightening enemy? I know that if this latter idea was true, the messages are that they have learned that death isn't such a bad thing after all and that his sacrifice (like their own) would be so valuable to the world... but how hard for them to think they were sending their own son to die at the hands of a murderer at 17.

I am asking if there is evidence from the books or JK Rowling - not merely for opinions. I hope that I have successfully taken these thoughts and boiled them down to one question successfully.

Edit: The suggested question is extremely close to mine, and if I had found it when I searched I mIght simply have accepted the answer because that answer addresses the bulk of my question even though the question was different (as often happens). However, in writing my question and looking at comments on it, I am still interested to know if it is possible that Harry's family and friends could have known that he would not truly die.

Answer 1

I think you confuse the order of events. Harry was able to open the snitch containing the stone because he had already accepted the inevitability of his own death in the first place. He accepted the need to sacrifice himself in order to destroy Voldemort's soul inside him in order to give his friends a chance to win. It was his own decision, partly influenced by these words (by Dumbledore, from Deathly Hallows):

The true master does not seek to run away from Death. He accepts that he must die, and understands that there are far, far worse things in the living world than dying.

As the inscription on the snitch said:

When his parents are saying they're proud of them, they're most probably referring to his bravery - for the reason in paragraph above.

As for your title, they couldn't have known he'd be back. From his conversation with Dumbledore at "King's Cross Station" (this quote is from the film, but I remember it to be faithful to the source):

Harry: I have to go back, haven't I?

Dumbledore: Oh, that's up to you.

Answer 2

I think they did know that he would survive, for the simple reason that Harry knew he would survive, subconsciously.

When Harry is at "King's Cross Station," Dumbledore never actually tells Harry about why he survived, Harry comes to all his own conclusions.

“Explain,” said Harry.

“But you already know,” said Dumbledore. He twiddled his thumbs together.

...

“But if Voldemort used the Killing Curse,” Harry started again, “and nobody died for me this time – how can I be alive?”

“I think you know,” said Dumbledore. “Think back. Remember what he did, in his ignorance, in his greed and his cruelty...”

Then the answer rose to his lips easily, without effort. “He took my blood,” said Harry.

“Precisely!” said Dumbledore. “He took your blood and rebuilt his living body with it! Your blood in his veins, Harry, Lily’s protection inside both of you! He tethered you to life while he lives!”

And of course there's the case to be made that the "Dumbledore" in King's Cross station was a manifestation of Harry's subconscious thoughts about Dumbledore in any case ("Of course this is all happening in your head," etc.)

Meanwhile, the spirits of the dead tell Harry that they're a part of him.

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

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

And they know things that they would have no way of knowing on their own. Harry never tells them he's off to be killed by Voldemort, they all just seem to know that.

Presumably, they have some connection to Harry's thoughts or memories. If so, it's a good guess that they knew that Harry a good chance of surviving the encounter, even if he didn't know so himself.