Does anyone know the exact hours of sunset, sunrise, business hours and the time of change of weekdays in Skyrim?

Sunrise and sunset is about 6 AM and 6 PM, respectively. Businesses typically open at 8 AM and close at 8 PM.

As for the weekday changes, that is currently bugged. They are supposed to change at midnight, but they pretty much do it at random for all we know right now.

The days and time can desync if you have vsync disabled, or otherwise let the game have a framerate of more than 60.

That has been disproven, numerous users have reported that V-Sync or framerates play no part in the bug, and I confirm it on my end. Also, consoles experience this bug, too. They are not synced, period.