Remember that Watson also has to depress a physical button (the same buzzer everyone else uses). The eye to finger path for humans is about 200ms. It probably takes about 100ms for Watson to physically press the button. So Watson is about 100ms faster. But that also gives humans about a 100ms window in which to beat Watson. This means that you need to start your press 100-200ms before Trebek finishes his last word.
That's pretty good sized window for most people given you are reading the question along with Trebek. If the person who turns the light on is very consistent, I think a human who is good at this could consistently beat Watson.
Click timing is indeed very important but I do not think Watson has any special advantage there.
Nope, it has to press down on a physical button just like everyone else. Maybe it can move it's finger a bit faster, but...not much.
If it rings in every time there's no way it will win.