If you can bomb down a trail on a fixed gear, then you are a mountain biking god!
To stop you can lock up the rear wheel and skid to slow down (while using the front brake too) or you can simply resist the forward motion with your legs, but it will take longer to stop that way.
Fixed gear mountain bikes are extremely rare - I have never seen anyone riding one.
There is no advantage, that's why there aren't any stock fixed gear mountain bikes. The five people who ride fixed gear offroad do it for the challenge.
There are plenty of people who ride single speed. There actually are some advantages to it although gears work better in some situations. (Go to the single speed forum for more information).
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