From the Balanced power Plan:
Sleep After 15 min: OK
Allow Hybrid Sleep: OK
Hibernate after: OK
Allow wake timers: Disable it, and check the Scheduled Tasks for any coincidence on auto starting the computer... may be nothing to it but better keep it disabled. wake timers are to enable programmed auto starts for instance if you want the computer to be on at a given date and time... say you want to access it remotely, or want it to be on the moment you want to use, etc.
S4 Sleep State is Hibernation and it's disabled according to your screenshot so it shouldn't be going on. Hibernation can only start the computer with the power button... though the MSDN article says the keyboard can start it.. so I suppose that's according to what improvements and settings a motherboard BIOS includes.
On S5 Says MSDN.Microsoft.com: "The system appears to be off. This state is comprised of a full shutdown and boot cycle"... so both S4 and S5 should be disabled and any setting that includes S4 and S5 should be disabled... Only SI through S3 should be enabled, and to prevent the computer from waking up when touching the keyboard or mouse, disable your peripherals from the Device Manager device properties > Power Management... but to retain some control to wake the computer with the keyboard, you can program a specific key in the BIOS. Usual devices are Network Adapter, Wake on LAN shoul also be disabled in the BIOS, also keyboard, mouse, you might also find something to apply in this article, or in any other from the Google search results below.
On your d) Check Read Bit: Enabled, if you have an SSD it may cause issues during S3 resume. Check full comment.
http://forums.hexus.net/motherboards/264957-asrock-ami-uefi-tweaking-guide-piledriver-chipsets.html
One detail I don't agree with from your comment on S3, is no LEDs should be blinking... If a LED is blinking, it may not be going into sleep mode when it wakes up 10 min later and goes to hibernation. Sleep mode in State S3 should appear to be completely shut down... but touching the keyboard, specific kbd key, or mouse which-what-ever you configured should awake it. BTW is your computer not in a closed room, where no one even a dog, cat, can touch it, or something like a frig starting can cause a vibration that wakes it?.. S3 state can be very sensitive and any shaking or vibration of the desk can awake it.
How to prevent your PC from waking up in sleep mode
http://www.pcadvisor.co.uk/how-to/windows/how-prevent-your-pc-from-waking-up-in-sleep-mode-3433604/
System Power States
https://msdn.microsoft.com/en-us/library/windows/desktop/aa373229(v=vs.85).aspx
https://www.google.com/search?rlz=1C1AVNE_enMX703MX703&q=list+of+peripherals+to+wake+a+computer+from+sleep+mode&spell=1&sa=X&ved=0ahUKEwiYyMm2hfzOAhUS22MKHb3gCzcQvwUIGigA&biw=1280&bih=653