Enabled by default on most clean installations of Windows 10, Fast Startup essentially hibernates the Windows kernel and loaded drivers to help slash startup times. It all sounds great, but Fast Startup may not be quite as good as you think. Not only can it seriously mess up dual-boot systems, it may also interfere with the installation of updates, and could cause problems with encryption software.
That doesn't say much about stability. The updates is the only thing that's going to be relevant for 90% of users, and all it means is that you should remember to conduct a restart after updates and not think that shutdown+start is equivalent to a restart.
However, I personally have noticed some other form of strange behavior caused by Fast Startup. I wrote this in my original post, but decided to remove it because I can't remember what exactly the problem was. It had nothing to do with any of those examples from that article. I wish I could remember what it did, but after that I started disabling Fast Startup as a precaution.
On a slow PC Fast Startup can make an impressive difference. On a fast, modern PC, it's probably not worth it.
Fast boot in BIOS isn't a good idea because what if you need to get into the BIOS sometime but won't be able to until you reset the CMOS.
Fast Boot in the BIOS is a setting that allows it to skip certain stages of POST.
Fast Startup is a form of hibernation that dumps the contents of the RAM onto the HDD/SSD and copies it back to the RAM on the next boot to speed up the initialization of Windows.
Be aware that Fast Boot can sometimes make it impossible to access the BIOS or boot menu via keyboard hotkeys. "I enabled Fast Boot and now I can't access the BIOS" is a common complaint. In this event, if you're using UEFI mode, you can initiate a restart to the BIOS from within Windows (8, 10).
I find that Fast Boot usually has a negligible effect on overall boot time, so I never bother enabling it. To get the fastest possible boot, you want to install Windows 10 in UEFI mode, with the BIOS set to UEFI and CSM disabled/secureboot enabled (assuming UEFI GOP GPU etc.).
There's no point disabling hibernation if you aren't short on space and want to use Fast Startup.
What is your motherboard?