Does your partner:
* Look at you or act in ways that scare you?
Okay. Won't deny that Edward does this. But he's a vampire. Scary by nature. It's supposed to scare you when he looks at you. Neither here nor there. Being "scary" is not abusive. I don't care what the NDVH says.
* Control what you do, who you see or talk to or where you go?
"Stay away from the werewolves. I love you."
Part one of "you can't apply the same old rules to this unique situation." You're really arguing that “stay away from werewolves” is abusive/controlling? Werewolves are dangerous. In particular, Jacob is more dangerous for Bella than Edward is. Jacob is a nineteen-year-old, freshly made werewolf who has not yet learned to control himself. Edward is a 300-year-old (right?) vampire who has learned, not only to control himself, but to not feed on humans. "Stay away from werewolves" is not controlling or abusive. It's good advice, which Bella pointedly ignores.
* Make all of the decisions?
Part 2. Who should take who's advice: the eighteen-year-old girl who WANTS TO HANG AROUND WITH DANGEROUS MONSTERS or the 300-year-old monument to self-control? Also, untrue. Bella makes the decision to become a vampire. Edward is against it from beginning to end, but eventually gives in because it's what she wants. Other examples include: what to do with the baby, whether or not to run from the Volturi and whether or not to allow Jacob around the baby, whether or not to allow Jacob near Bella, and whether or not the werewolves in general are to be trusted. All things Edward and Bella disagree on, and all things that go Bella's way.
* Act like the abuse is no big deal, it's your fault, or even deny doing it?
"If I wasn't so attracted to you, I wouldn't have to break up with you."
How can breaking up with someone to protect them from yourself possibly be considered abusive? Healthy? Maybe not. Abusive? No. Edward is a vampire and doesn't trust himself to be around Bella, and doesn't want to see any harm come to her.
* Threaten to commit suicide?
"I just can't live without you. In fact, I'll run to Italy and try suicide by vampire if anything happens to you."
Edward never threatened to commit suicide. He tried to commit suicide, without a word to Bella. He would have died, and she would have thought he kept doing the “immortal vampire” thing, had his sister not intervened. Threatening to commit suicide can be considered psychologically abusive and a cry for help. Attempting to commit suicide and not telling anyone about it... not so much.
* Threaten to kill you?
On their first date.
Again, unique situation. Edward never threatened to kill Bella. He warned her that she should stay away from him because he might unintentionally cause her death. According to the letter of the law, I suppose this is technically a threat, but the connotation of a threat is that there is intent behind it.
These are some more signs of an abusive relationship.
Has your partner...
* Tried to isolate you from family or friends.
Bella doesn't have time for anyone else!
Bella's choice, not Edward's. On at least one occasion, Edward suggests that Bella ought to spend some time with her friends or her father.
* Damaged property when angry (thrown objects, punched walls, kicked doors, etc.).
No argument here. Edward has super-human strength. When he gets angry, things break. Things: not people. I break things when I'm angry too. I don't get angry very often, but when I do, I find something that will make a satisfying “crunch” or “boom” when I put my fist through it. I've never attacked a human being out of anger in my entire adult life. That doesn't mean I abuse my wife. Granted, this can be an indicator of an abusive personality, but not necessarily.
* Pushed, slapped, bitten, kicked or choked you.
Does tossing her through a glass table count?
No, it doesn't. When in a house full of (friendly) vampires, one of whom is only newly “vegetarian,” Bella accidentally cut herself. Reacting quickly, Edward threw himself between Bella and harm (in the form of his “brother” Jasper), accidentally knocking her over into a table. This act of defense should not be confused with an act of aggression.
* Abandoned you in a dangerous or unfamiliar place.
"We're breaking up. And I'm leaving you in the forest."
Yep. Absolutely happened. Total asshole thing to do. Unquestionably an act of abuse.
* Scared you by driving recklessly.
Super-human reflexes. While Bella may have been scared, she was not in danger. If I bring a new girlfriend home and my dog barks at her and she gets scared, does that make me abusive? New girlfriend is in no danger from my dog, but feels afraid, and has every reason to believe that she is in real danger.
* Forced you to leave your home.
She had to run away with him to flee from the other vampires in the first movie, and she had to drop everything and run to Italy in the second.
First of all, Bella was fleeing from danger, not running away to elope. She did not flee with Edward. She fled with two of his adopted siblings. Edward didn't “force Bella to leave her home.” He helped her flee from a ruthless murderer. She didn't have to go to Italy. If it were up to Edward, she wouldn't even have known he had gone there, he would be dead, and she and Jacob would have a long and happy life together. Bella knew all of this and chose to go to Italy to save him, even knowing that she stood little to no chance.
* Prevented you from calling police or seeking medical attention.
Check. Even in the hospital, nothing is a big deal.
Wrong. After the dance studio incident, Edward and his family (one of whom has been a practicing physician for centuries, and knows what's “a big deal” and what isn't) not only brought Bella to a hospital, but they called her parents (one of whom is “the police”) to let them know she had been injured. Which part of that is abusive?
* Views women as objects and believes in rigid gender roles.
Well, they are Mormon... (I know, I know, cheap shot.)
Yes. Absolutely a cheap shot. Personally, I'm impressed when an author can write protagonists that don't share their values. If you want an example of a strong woman in a leadership role, look no further than Alice, Edward's “sister,” who practically runs the family.
* Accuses you of cheating or is often jealous of your outside relationships.
Again, you're really arguing that “stay away from werewolves” is bad advice? Also, patently non-true. Edward is nothing but supportive of the notion that Bella should have friends outside his family. For the first two (three?) books, he encourages her, at every turn, to have nothing more to do with himself. He does not accuse her of cheating, and is not “jealous” of her relationship with Jacob. He knows what Jacob is and thinks (accurately) that Jacob is dangerous to Bella. I don't want my wife to hang out in prisons or lion cages. Not because I'm jealous, but because those are dangerous places. If I found out that she was visiting those places, I would be a lot more upset than Edward gets when Bella refuses to stay away from Jacob (one more instance of Bella doing something Edward doesn't want her to do).
All this being said, do Edward and Bella have a healthy relationship? Probably not. Is Edward abusive? Not by any of these criteria. Okay, there was that one. Can't refute that Edward left Bella in the woods. That was a total dick move.