The automatic starting after shutdown has been a problem for over a year now. There are other threads that have talked about this for pages. Basically, the only solution is to disable the wake on LAN function in the bios. Unfortunately, if you need the wake on LAN function, you are out of luck. Since the issue was initially reported, Intel has released several BIOS updates, but none of them have fixed this problem. It is unique to the NUC, and quite frankly, an embarrassment to the BIOS engineers, in my opinion. I have tried everything myself including BIOS updates, and resorted to simply disabling the wake on LAN.
as for your other problem, I have never heard of that issue, so don't have a solution. I don't use sleep/hibernate myself. You might want to simply disable sleeping and hibernating, since the NUC fortunately consumes very little power when idle, sometimes less than 10 W depending on the setup. The funny thing is that all of these issues disappear if you simply leave the NUC on all the time without any sleeping, hibernating, or shut down. Not exactly a great solution, I know.