Control iPhone from Windows 8
No, there is no general purpose remote control on iOS. I don't follow the jailbreak community closely, but you might get some other capabilities there.

From a non-jailbroken scheme, you have these small elements of what you ask:


Air Parrot type software to AirPlay a PC but no capability to remote control
MDM tools like Casper Focus to remotely place an iOS device into guided access mode or automate the opening of one URL.


Again, the MDM profile isn't anything that hooks into VNC or accessibility (software switches or accessibility features like voiceover) - it just simulates one action to launch an app.