jimmie,
Not an expert, but:
Backing up your database locally, depends on what you mean by locally. The database itself is on a hosted server, so you can back it up "locally" on that server. You might be able to back it up to your actual local hard drive, but I think that would be complicated. I haven't cancelled my backup subscription to AC, so the database (but not the imported items) gets backed up daily from the cloud hosting to AC itself, but that's probably overkill. Seems to me that a commercial hosting service like the one AC cloud uses should be backing up frequently and safely. I hope I'm right. And since I no longer back up the imported items like I used to when it was running in my office, I am depending on the hosting service.
If someone else (like your nurse) is connected and a second person logs on from another computer, the first person gets unceremoniously kicked off with a notification. I believe that when that second person logs on, the program will resume exactly where the first person was, without losing their information and without having to log back into the AC program, but I'm not 100% sure about that. Again, there can only be one person logged on per connection. You purchase the number of connections.
As for integrating with a billing service, no idea how that would work.
Michael