Did she kill him? (spoiler)

Yes. She remembered that she needed to cock the gun to put a bullet in the chamber and you hear it go off and a body drop. He couldn't resist the fact that knowing she was a nymphomaniac that she did not want him after her revelation and owning her addiction. In the end as good of a man as he seemed it didn't stop him from doing what many men would do to a woman like that and pray on her weakness and addiction. Hope that helps somewhat !!

THERES NO ROOM IN MY CIRCUS TENT FOR YOU !!!!

The possibility of Joe killing herself is there. Even though the subtitles for hearing impaired states "zipping up her trouser" at the end after the shot. But it would then be strange for Seligman to walk out quickly and leave the apartment.

Also, the ending is quite strange. He being an asexual, and coming in to her bed without being erected. Why would he even try when he wasn't horny? And why would she react by shooting him? She had history of raping the man on the train, by oral sex. And she had orally pleased the pedophile, just because she saw herself in him, and pitied him. One answer could be because she had opened her up so much to him, and was overly tired, and extremely vulnerable. Either way, the question to if or if he was not trying to rape her is also at hand. He surprised her and came quite silent on to her, but used no force.

So to conclude your question: Only Lars Von Trier knows..