1. Value is in the eye of the beholder. Heart-shaped diamonds will cost less (say 25-50% less) than same-weight/colour/clarity rounds, and sometimes have a larger face-up size, but they don't look as brilliant or fiery and they are intrinsically less symmetrical, which some people don't like, and that makes them somewhat more difficult to use in jewellery.
2. I assume you mean sparkle, fire and contrast, yes? Generally less in hearts than in rounds, but it is hugely variable with the quality of cut, and you have far fewer indicators of that on hearts than on rounds (not least the relative rarity of comparison stones: there's about 1 heart every 50 rounds offered for sale).
3. Same as any other diamond.
4. The big problem with fancy shapes (anything other than round - but heart is the ultimate fancy shape) is that you have no indication of the cut attractiveness and beauty other than by direct observation, and there are more variables that determine appearance (cleft depth and sharpness, roundedness of lower part, shape of the point) which in turn give personal taste a greater role in choosing a stone over another one.
Edited by davidelevi, 24 November 2011 - 10:25 PM.