Does Molly, Arthur, Lupin, Sirius, or anyone else realize the full contents? Did Sirius know when the Potters went into hiding? Is Dumbledore the only one knows that Harry might have to die?
No “major” characters except Harry and Dumbledore.
In Half-Blood Prince, Dumbledore says to Harry:
“There are only two people in the whole world who know the full contents of the prophecy made about you and Lord Voldemort, and they are both standing in this smelly, spidery broom shed.”
Harry never tells the full text of the prophecy to anybody else (at least, not in the books), and Dumbledore seems unlikely to tell anybody either.
However, at least one other person may have heard the full text.
As Dumbledore explains to Harry at the end of Order of the Phoenix, the Ministry copy didn’t always have his name on it:
“The official record was relabeled after Voldemort’s attack on you as a child,” said Dumbledore. “It seemed plain to the keeper of the Hall of Prophecy that Voldemort could only have tried to kill you because he knew you to be the one to whom Sibyll was referring.”
The only way the Keeper could have known to do this would be if he knew at least the first part of the Prophecy. It’s not completely impossible that he might have heard the rest.
"No, they do not," interrupted Dumbledore. "There are only two people in the whole world who know the full contents of the prophecy made about you and Lord Voldemort, and they are both standing in this smelly, spidery broom shed. It is true, however, that many have guessed, correctly, that Voldemort sent his Death Eaters to steal a prophecy, and that the prophecy concerned you.
Thus according to Dumbledore only he and Harry know the full contents of the prophecy. It is not implausible that who ever transcribes the prophecies for the Departments of Mysteries
may know it's contents as well, but that's just speculation.
From the book its clear that Dumbledore is the only person to know the full prophecy. He then reveals it to Harry, who chooses to tell a few people. Snape knows a piece of the prophecy which he told to Voldemort, and Voldemort or snape may have told this partial piece to other death eaters, as we know that Bellatrix targeted the long bottom family as she felt they had some connection to bringing Voldemort back. Sirius, molly, arthur, lupin may not even know their was a prophecy as Dumbledore doesn't reveal anything to others who have the potential of getting caught/tortured and revealing the prophecy.