The function of there in this kind of sentence is to introduce a new topic. Because of this, it is usually followed by a form of the verb to be, but looking at Google Ngrams, it's also often followed by verbs like came, stood, lived, which are natural when introducing a new subject.
So Googling, you can find sentences like:
Across the street an arc-lamp shed its cold rays. And into its glare there strode a man draped in a yellow mackintosh.
However, people don't usually dance onto the scene, so there danced a man would be a very unusual sentence in English, and it sounds quite odd. If you want to formulate this sentence with there, it would be much more idiomatic to say
There was a man dancing in the hall,
and if this man has not been mentioned before in the narrative, this is an idiomatic way to phrase it.
And to answer your other question,
There died a man in the hall,
sounds equally odd.