The hydrometer reading will be different yes. It will read lower, because the enzyme will help lower the FG of the brew, resulting in a higher alcohol content with less residual sugar.
If you're asking the the reading will be false then the answer is no.
Negative density. Your should consult your friendly local physicist.
The interesting thing is, a reading of 1.000 doesn't mean there is no sugar left in the liquid.
Alcohol has a density less than that of water, and in a 5% abw beer a hydro reading of 1.000 means you have roughly 2.6 g of sugar in 100 g of beer.
Kronic, I don't think anyone can safely say. Once you get the same reading over 3 consecutive days it's probably done.