I wouldn't disturb the fermentation until you're sure it is complete. The suggestion might be two weeks, but it always depends on gravity, temperature, type of yeast and amount of yeast pitched. The best way to ensure it's done is to take a gravity reading.
If you're dry hopping with pellets, then I would definitely recommend using a sack. they are kind of a pain to get out, but the pellets turn into a hop sludge that is difficult to rack off of.
Not all chemicals are bad. Without chemicals such as hydrogen and oxygen, for example, there would be no way to make water, a vital ingredient in beer.