Does Bitcoin have legal status as a corporation? If so, what kind, and in what jurisdiction(s) is it registered?
No. The whole point of Bitcoin is that it is decentralized and there is no single corporation behind it.
The debate of bitcoin in the legal system is just in the beginning. It's not even that clear (worldwide) whether bitcoin is legally consider money or not. Up to now, most of bitcoin space is unregulated (including the issue of corporation status).
But this doesn't mean that it will be unregulated forever. Nobody knows what the future holds, maybe one day the government might decide to debate whether miners should be responsible for bitcoin issues (as one day happened with Napster, Torrent and several other internet sectors).