I updated manually a few days ago. Is the updater going to recognize this and stop prompting to download 0.5.6?
Yes. The Auto Updater loads the MWLL version from the info.xml file, located in MWLL's root directory.
As for the Auto Updater downloading slowly, that can be because of any number of reasons which make your system torrent-unfriendly. As of Auto Updater v1.0, you can tell the Auto Updater to use a HTTP-based downloader (called Parallel HTTP) instead of the bittorrent-based one. Just open the Settings window, and find the option "Use downloader".
The Parallel HTTP downloader is nowhere near as solid as the bittorrent one, so you may experience some instability (in the form of an occasional crash). Just restart the updater, and it should continue from where it left off.