Hi Laura
Regarding the medical stuff I had been under the impression we had to undergo all of that as well as part of the visa conditions but I got mine granted without any condition. I even contacted the London office of Aus Immigration to make sure and they said if I was granted it then that was it. I don't know about the states with/without limited reg as I assumed it was statewide with the new national board...sorry!
All the paperwork is pretty frustrating and you begin to think if it's worth it sometimes...they really don't make it easy!!
Good luck with it!!
Aoife

PS I didn't state any hospital on visa application just said I was a physio searching for work so didn't know yet