No, they only stop laying during the molt. Some of mine will keep laying through most of the molt though, and just stop for a week or so at the peak. They will continue laying normally (sometimes better!) after their molt. Molting is also a chance for layers to take a short break and "recharge"...
Well, I free range all my birds on 6 1/2 acres, so I probably just don't notice how many feathers are actually there. :P But I guess if I think about when they were cooped up way back when there could be a lot of feathers.....
It does not hurt the chicken at all. It is similar to a dog shedding.
You will find some feathers scattered around, but usually not too many.
Chickens will not molt their first fall/winter. So, a chick hatched, say, March 2012 will not molt until fall 2013.
The purpose of molting is to...
It sort of depends on the chicken. Some will have a REALLY hard molt (like, totally bald), and others you might not even realize are molting.
Here are some pics of a pretty normal molt (not my pics, my camera is broken, but this is what about 20 of my hens look like right now):
And...