Sixteen days sounds about right (better than the 10 days some kits recommend). To be sure, you need to take gravity readings and get the same result for three days straight. With a kit, though, you're usually pretty safe to just follow the directions that came with it.
Once fermentation is done, the yeast will start to consume whatever fermentables they can get, which in most cases is some of the more complex sugars and fermentation by-products. The longer you leave the beer in the fermenter, the more yeast and trub will drop out of solution, leaving you with a clearer beer. Your beer should be fine for up to two months in the fermenter, so there's no hard deadline for bottling. Of course, after you bottle you have to wait a couple of weeks for the bottles to carb up, so the longer you wait the longer it'll be until you can drink!