Aero is often a short for aerodynamic, and there are several bikes that can be said to be aerodynamic to some degree.
Yes, BMX bikes were used in the 2008 Beijing Olympic and is going to be used in the 2012 London Olympic.
Question doesn't quite make sense, as Mountain Biking is also an Olympic sport these days, meaning there are Olympic mountain bikes. I guess you are talking about road bikes vs mountain bikes. Road bikes are more efficient - for road riding - because they are lighter, have lower rolling resistance, a more aerodynamic riding position and doesn't lose any pedaling energy to suspension in the frame or fork. It's not really a fair comparison though. A MTB ridden off road will be more efficient than a road bike ridden off road.
Due to stronger and lighter materials, the bikes have gotten lighter. Due to careful design and analysis, they roll easier and are more aerodynamic.
Coaches
Snowboard cross
Bikes and helmets can be made lighter more aerodynamic. Drive-trains can be made more efficient.
Yes. The road bikes and MTBs have multiple gears while the BMX and track bikes only have one.
Airplanes... Race cars... Spears... Bullets... Speed bikes... Racing motorcycles... Bicycle racing helmets... There is an endless list
No single person invented the olympic bike, it was a gradual development from the bikes produced for ordinary use. Eventually competition rules started regulating the design of the bikes as well, with wheel sizes, minimum weights ASO.
An aero bar increases the aerodynamic effect of a bike, and in some cases, can contribute to greater performance through better efficiency and speed. They are sold wherever bikes are sold.
Aerodynamic simulation