Is there a way to find whether the user using Date & Time as Auto or Manual.
i.e., to find General -> Date & Time -> Set Automatically is ON or OFF.
Is there a way to find whether the user using Date & Time as Auto or Manual.
You cannot access user's settings (except those of your app) by code.
So it is likely you don't have access to them either.
You have to tell user to check settings:
Assuming you are referring to macOS, you could run the systemsetup command via a privileged helper to interrogate or modify the Date & Time settings.
See 'man systemsetup' for documentation of the command.