I think it's easier and faster to pedal a Bananna-seat bike than a 10-speed because the legs are not as vertical and the chain on the Bananna-seat bike is longer, hence more power?

I also would like to know how far and long can a biker go uphill without having to stand up and pedal. Again, I would think a Bananna-seat is better because the biker is not as vertical. Then again, a Bananna-seat bike has no brakes.

Could the Mythbusters test out various bikes and biking positions to see which one would be the easiest and fastest to bike for distance, uphill, downhill and stopping on City Street?

* 10-speed racing bicycle with curved handlebars and the biker bent forward
* 10-speed mountain bicycle with horizonal handlebars and the biker vertical
* One-speed horizontal handbar bicycle (like the ones you see in China)
* One-speed Bananna-seat bicycle (like a girl's bike)
* Fancy exercise-bike that looks like a Chopper with the legs and pedals really forward and the biker leaning back.

* Race them all against a two-seater bicycle?

Where have you been for the last 30 years? That's about how long it's been since a "10-speed" roadster was the norm.
Contemporary road bikes have as many as 30 gears with a 10 speed rear cassette and a 3-speed crank.

There's essentially no comparison between the efficiency of a properly-fitted road bike and a single-speed kid's bicycle.
With the proper selection of gears, a rider can climb a mountain in the lowest gears, and go down the other side at 60 mph plus.
One can pick precisely the right gear for nearly any condition.

The rider's position on the bike is a matter of technique; your descriptions have little relation to real-world cycling.
On a roadster, the normal riding position is with the hands on the brake hoods, the upper body inclined at about a 45 degree angle.
One only goes down into the "in the drops" position when trying to sprint or cheat the wind.
The normal climbing position is more upright, with the hands on the top portion of the bar.

The Tour De France is currently running, catch a stage or two on the VS network. See how the pros do it.

The most efficient bike is simply the one that puts the most mass on the crank and then balances the crank between the front and rear tires so taht heavy down forces are carried evenly between both tires.

The road bike gives the rider the easy advantage to choose between sitting and "running in place" where he can stand on the cranks and put his whole weight down each time he pedals the crank.