Dick and Barbara had dated in New Earth and after doing so came to the agreement they weren't good for each other. They broke up naturally as part of the narrative. They weren't together. This is opposed to Dick and Kori, who had a forced separation under editorial mandate. The only conceivable way for them to not be together was to have them not talk to each other even when standing in the same room, after declaring they loved each other.
Babs showed a lack of respect for Dick as Batman during his run, at a time he needed cooperation and communication the most. He has shown continued affection for Starfire even after telling her he didn't love her. He sows no hang ups over Barbara. Barbara is emotionally manipulative and needs someone that doesn't take her crap. Like how Catwoman wouldn't take Bruce's and vice versa. Dick is too honest and forthright. His main flaw is a lack of commitment which he had overcome, he did become Batman and committed to training Damian, which would likely take 5 to 7 years.
Hmmmmm, I wouldn't go that far. There's a lot of hate for the New 52, and I can certainly understand it, but I wouldn't say it's completely irredeemable. Yeah, some things are totally whacked-- like the age differences between all the Robins and how Tim apparently never was one wtf-- but there have been good stories. You just gotta know where to look. XD
I think Scott Snyder's run on Batman has been pretty damn good. The finale of the Court of Owls arc was ridiculous, but the rest of it was great. Death of the Family is a pretty amazing arc, too, across the board. I'd pick up every issue of that arc in each series it appears in, if it's possible.
Animal Man and Action Comics both had pretty strong starts; I'm not sure if they're still any good because I had to stop reading them because I'm poor. The first arc of Aquaman was good, too. (That's like one of the only Aquaman stories outside of the JL that I've ever actually read, tbh... XD
And, being a loyal Bat-fan, I still pick up Batgirl, Red Hood and the Outlaws, Nightwing and Detective Comics. I used to read Teen Titans, too, but that story is terrible, so I stopped. I actually like Red Hood and the Outlaws, which pits me against a lot of people. The art for the first 10 or so issues was absolutely gorgeous. The story wasn't terrible, either... just a little shallow. Maybe I'm biased because I love Jason Todd, but I like the characters and their interactions in the story.