I think the heart probably is Kathryn’s. That would be awful, but bad things happen, and fairy tales are not just puppies and hugs. I mean, look at early versions of Red Riding Hood, like Perrault, and look what they did with it here. Gruesome and awful things do and will happen (and have happened) in the fairy tale land.
And I think that it is obvious and self-evident that the hearts are literal hearts that still have a magical connection to the person. This is magic, after all. The Evil Queen literally shoves her hand into the Huntsman’s chest and rips out his heart. That isn’t metaphorical; she is ripping out his actual, human heart. The only reason it works is magic, and the only reason Regina could kill Graham that way is that she still had his heart. I am sure she doesn’t have magic, at least not at the same level of power that she does in FTL, nor does Mr. Gold.
We know from several little things that magic does function on some level, but not to its full extent. The best recent example is Ruby’s heightened senses and Granny’s arm that hurts each full moon. So clearly werewolf affliction still exists, and affects them in some way, but Ruby isn’t turning into a wolf (at least, we have no indication that she is).
So I think Regina can either do some magic, or can work with magical artifacts from FTL, but can’t cast spells as such, or do very much. If she could, she would have done something to Emma on day one. She has to know that with what Henry believes (which she knows is true), letting an outsider mess around in town with him has got to be counter to her plans. So if she could do magic, she would have. Similarly, I think Mr. Gold can’t do magic. He doesn’t look like Rumple and there have been many occasions in which magic would have served him greatly. But neither of them ever use magic. The only magic we have seen comes straight from FTL.
So I think it’s a real heart, and it is Kathryn’s heart, and that Regina can’t do magic on her own in Storybrooke with which she could pull out Kathryn’s heart and use it for something other than framing a murder. I can’t think of a reason for the Evil Queen to have taken Abigail’s heart in FTL. If it isn’t Kathryn’s, it is Graham’s that Regina just still had after killing him.