Let the bike rool without the pedals moving, I like to stand on the pedals and get my but off the seat for a little air and blood circulation when going down hill
Fixed gear riding will improve you're pedal stroke by letting you know real quickly when your not pedaling smoothly. I ride my fixie in the colder months because I am not out for long rides and I feel I get more of a workout in less time because I can't coast and when I am going down hill I am either resisting the pedals to keep my speed down or just going with it and spinning at very high rpms. Some people myself included find fixed gear riding to be just plain fun. The ideal set up is a flip flop hub so you can ride your bike either way. I will use the freewheel side if I am commuting or just out to tool around.
You could go brakeless on a fixed gear, but it's both illegal and ill-advised. It should have a front brake, at minimum. If you run a freewheel, you'll need two brakes.
Single speeds, and bikes that come equipped with a flip-flop hub generally have more relaxed geometry than purpose-built fixed track bikes. That's a consideration when you see your dream frame/fork combo advertised as a track bike.
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