First, I just wanted to say that I
really like your idea and will shamelessly be plundering it for my own campaign when January rolls around and I get back to playing
What should the demiplane be like?
Here's a thought -- what if there isn't a plane. What if the stone itself is sentient and the heroes are projected impressions of real heroes who have handled the stone in the past -- memories given life via the stone? If you go this route, when a hero disappears, they don't return to a demi-plane but, rather,
cease to exist temporarily, retracted by the stone for its own mysterious reasons.
Are there more than one hero stone?
No -- but there is a
Villain Stone
What should it be called?
Give the stones proper names of some kind, though no voices to go with them -- they communciate their will via the heroes or villains that they project.
And how do I present this to my players in a way that doesn't make it seem like a curse?
Set the campaign up so that the stone acts as a kind of silent patron, racing against time to stop the villain stone from doing Really Bad Thing X. The heroes, so far as they're concerned, are real, living, beings -- they don't know that they cease to exist when they disappear, they merely can't recollect what has happened to them when they're not being projected into the physical world.
The key here is that the player's actions dictate the will of the hero stone. Don't try to force some pre-scripted weirdness on them. Let the larger campaign unfold according to their actions. That said, you
can influence events by way of the villain stone, as you (being the DM) have total control over its will and how it manifests in the campaign.
So far as the players are initially concerned, they may merely be adventurers doing their thing -- but every now and again, the villains that they come up against should be manifestations of the villain stone, providing a plot hook for the larger story arc and the players' eventual discovery of the secret war that they are part of.
[Note: Incidentally, this also sets up the PCs to be the equivalent of Iconic NPCs in most campaigns. They may occasionally be recognized by people as the heroes of legend that they are modeled on, though the PCs are merely convinced that people are mistaking them for somebody else (remember, PCs have no idea that they are projections of the hero stone modeled on epic heroes who had come into contact with the stone in aeons passed).