Does Rolling Stone require three empty squares between it and the nearest hero when it is first played, or does it need only two empty squares (with the stone being in the third square) between it and the nearest hero when it is first played?

Text on the card: as long as it's at least 3 spaces away from the nearest hero

So there need be only two spaces between them. Adjacent = 'one square away'.

I would agree with Inle. Although they don't use the word "range" in the text, the method of counting distance should always be consistent, and a target at Range 3 would have two empty spaces between the hero and itself.