be careful digital ground isn't always the same as the chassis ground, and often you'd use a pull down resistor, depending on the design its typically 0-10k ohms ( a 0 ohm resistor is basically a wire in a resistor package )
i'd imagine whatever driving that line is protected so overriding it probably won't hurt it, if its normally high it'll probably have a pull up resistor instead.
you would have to have it switched on, yes.
grounding it with a wire or resistor will cause it to bounce like crazy, ie make and break the connection thousands of times, what effect that will have is difficult to predict
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