1. I have no idea what, exactly, gets stored as part of the system state hibernation and it looks like this feature is, for all practical intents and purposes, just another way of having full conventional hibernation at shutdown, but without calling it that. Why they did this only Microsoft knows.
The new feature for "starting where you left off" is, I believe, limited to Windows 10 Pro, but I am not 100% sure about that. I do know that Fast Startup was re-enabled on my machine, but not by the Fall Creators Update itself, but one of the subsequent updates. I can tell when this happens because my shutdown time becomes slower and my startup time much faster. I've said many times before that, for myself, I don't want shut down to be some perverse (in my opinion) variant on hibernation - I want the machine to completely shut down and for Windows 10 to reload from scratch from disc when I power up again.
2. The warning message about others being logged in when you attempt to shutdown (at least when Fast Startup is disabled) or restart has been around since long before Windows 10. I have never had it come up except when more than one user is logged in to Windows when an attempt to shutdown or restart is made. Are you certain that you are logging off from the userid after having closed all the programs it was running when you have had two different userids logged in? Just being logged in, with no programs running for the userid, will still cause this message to be triggered.
3. The only way anything can be remembered between powerings-on is via being written out to disc and then reloaded. As I said earlier, everything about this "new feature" appears to behave exactly as conventional hibernation always did.
4. I cannot imagine why any user not logged in (and I don't count "System") would ever show up in task manager. I can imagine how this could occur if the machine is actually hibernating instead of shutting down instead. One way you could try to flesh out if that's what's happened, regardless of the mechanism of hibernation, is to do a Restart and see who shows up in the Users tab of task manager. A Restart forces a complete shutdown and fresh reloading of Windows 10 from disc. After that the only user you should see is the one you are logged in as.