Actually the red road bike is
fixed gear, which means that as long as the wheels are moving, the cranks are moving. Like track bikes(velodrome) and many bike messenger bikes there is no freewheel on it. Theoretically, you could pedal it backwards.
I just built this up for something to do with my old road bike and plan on riding it a good bit this winter. The bike is 20 years old, so it wasn't worth anything to sell, plus I love the older lugged steel frames and didn't want to get rid of it. Fixed gear riding is supposed to improve your pedal stroke by making it smoother. I have the bike geared with a 39 front/15 rear which should be good enough that I'm not spinning like mad on the downhills yet can still ride the uphills.
Single speed riding is lots of fun, especially on trails. It will remind you of how much fun riding was as a kid. You don't worry about being in the right or wrong gear, you just ride. There's also something about the simplicity of the bike that's cool. I haven't done much mtn biking lately because I've been training for a century ride(and with having a little kid, driving somewhere to ride takes too much time), but I'll get out some this fall. I don't want to sound too flaky but single speed mtn biking is an almost spiritual fun.
BTW,
Sheldonbrown.com is an excellent source for bike maintenance info and he's considered one of the best on the web.