If I want it to turn on in the morning, but then allow me to turn the light off and on as I choose during the day, is that possible without unplugging

Yes that can easily be done by simply switching the button from the"TIMER" position to the "ON" position.

Yes, assuming the switch controls an outlet (is what I'm guessing you are referring to). Mine is wired to my porch lights but I can turn them off or on at anytime including during the programmed hours.