SPOILER ALERT: This reply discusses the plots of "A Rose for Emily" and "The Metamorphosis." Please don't go any further if interested in reading these stories.

Tough questions.
I think there is a small line between the two. I agree with Tim's opinion, it is a cross genre and has a more mainstream quality.
"A Rose for Emily" is about a woman who dies and the townsfolk find out she's been sleeping with the corpse of a man she killed years and years ago. Sounds like horror, but most consider it literature, even Southern Gothic. It's dark fiction because the story's emphasis is the theme of times changing, the old South is no more and a new South is emerging. Emily's family has died out, and they were the most important citizens in the community. Because of his constant refferal to decay and death, lots of people tend to look past the plot and straight at the theme. The plot is certainly horror, but the focus of the story isn't on plot.
Kafka's "Metamorphisis" involves a man who wakes up one morning and is a cockroach. Now, the plot is 100% horror. A giant cockroach right? But, instead of focusing on the roach as a monster, Kafka focuses on the human condition. man as monster. His family cannot accept him as a cockroach, so they torture him. But, the story involves the roach's exploration of his feelings and doesn't focus on the torture throughout. Many consider this dark fiction because theme is more dominant than plot.
I'm not sure if that makes sense really. It's a truly mind blowing question. Also, fantasy with horror elements, romance with horror elements, speculative fiction, all of these I would consider dark fiction if the set up of the tale isn't primarily horrific. And by horrorific I mean something dealing with the senses to provoke fear. Atmosphere. If the story's intent is mainly to frighten or deeply disturb...that's horror.
For example: Look at
Silence of the Lambs v.s.
No Country for Old Men. Both deal with serial killers. But one deals more with theme than the other. One deals more with gore and is meant to disturb. Both are great novels, but only one is horror and only one is dark fiction.
As for the second question, in my opinion it's okay for either to have a happy ending.