Your diet is obviously also a factor here. If you start out at a healthy weight, you only need to gain somewhere between 20-30 pounds during your whole pregnancy, less if you're overweight and a little more if you're very thin. That's less than a pound a week spread out over 40 weeks. You only need an extra 300 calories or so daily. So if you actually try "eating for two" or don't pay attention to what you're eating, you might pack on more weight more quickly.
Depends on a lot of things, including the woman's size and whether or not she's already had children. Very thin or very petite women may show a little faster; heavyset women or women who carry high might take a lot longer than most.
Most women won't really "show" till after the first trimester. Generally speaking, the more kids you've already had, the faster it'll be noticeable because all your muscles and ligaments have been stretched out before.
It's common to have bloating and water weight gain right off the bat between about 5-8 weeks, but that's not baby yet. A lot of women actually lose weight the first couple months because of morning sickness and digestive problems, then make up for it in the later trimesters.