Can a Canon 580EX II be used on a Nikon D5000, and what features will I lose?

You have a lot of questions in your question, many of them un-answerable, but I'll focus on the title, "Canon 580EX II flash on my Nikon D5000". This can certainly "work", as in "function", but because the Canon and Nikon hotshoe contacts are different (apart from the center pin) and because the TTL "language" is different, you'll only be able to use the Canon flash in manual mode on your Nikon. There's certainly nothing wrong with that if you know how to use manual mode, but there are cheaper ways to get a manual-only flash with comparable power. It can work as an external with the SB-600, but not via Nikon CLS...you'll need to use a PC cable or optical trigger or other means of firing it (PocketWizard or similar).

Of course, the Canon flash will work quite well in automatic/E-TTL mode on the XTi and give you access to (nearly) all of the features including high-speed/FP, and AF assist beam (some of these require modifications to the camera settings).