How to tell if someone was using your iMac?
my work computer is always on in the morning. I turned off the Wake Settings in System Preferences/Settings... and I find my computer on and the Wake Settings are on again.
Sleep is unnecessary and should be disabled. Shut for long absences/idle overnights (i.e. do not manual-sleep), and for regular operation, use the settings exactly as shown here Wake up a remote Mac mini - Apple Community, should fix.