You've asked a number of questions about trains, so let me start by answering your first and fifth questions. Train engines turn some form of power into motion. They do this by using the power to turn the wheels of the train. One way to do this is to use gears to convert power from steam (for example) into the turning of the wheels. Another way to do this involves the use of side rods. For trains with side rods, the rods are used to turn the wheels. For old steam locomotives, the steam from the boiler would be used to push the rods, which in turn turned the wheels.

The first steam locomotive ran in 1814 and was designed by George Stephenson. This train was based on an 1804 design by Richard Trevithick. The first steam locomotive built in the United States to be used for regular railroad service was the "Best Friend of Charleston" (1830). The fastest steam locomotive was the A4 'Mallard' 4-6-2 and could reach 125 or 126 mph.

According to the 1997 Guinness Book of World Records, the French TGV had the highest average speed from one station to the next of 253 kph (157 mph). This includes the time needed for the train to accelerator and to stop. The train actually reached a top speed of over 300 mph. The Japanese have a new train which may break this record very soon. The new Shinkansen is also expected to average 261.8 kph (162 mph) between Hiroshima and Kokura Stations.

Trains are a fun subject, but I am not an expert, so if you would like to know more, I'm sure that there are a lot of books in your library which have interesting information. You might especially want to look at the history of how trains are powered. You may know people have used coal, diesel fuel, and electricity to power trains. A good book will tell you how each one worked and in what time period they were used.

Trains --
1. Old style steam locomotives did not have gears -- their steam engine was integral to the drive wheels on the engine. Modern trains (electric) locomotives do indeed have gears -- and much else besides. All modern train engines are electric -- even though they burn diesel (or coal oil). You can hear the engines speed up when the train approaches an up-hill grade. The question is -- why are they built with an engine, a
generator and several motors instead of the old style direct gears?
Hint: Trains have massive loads, widely varying track slopes and diesel engines have a fixed rate operation for peak efficiency.

2. The old steam engines were usually run well below 40MPH due to problems with maintaining the tracks-- but could go much faster. I seem to recall a 45 mile run before 1900 in which a locomotive pulled a train at better than 65MPH... (Stanley Steamer cars were known to exceed 75MPH).

3. The first practical train engine was built by Richard Trevithick in England in about 1803 -- earlier efforts had not have sufficient power to pull any sizeable loads. His engine was high pressure (about 150psi). (Rail tracks for carts originated in the middle ages for mines and other applications). A fundamental problem was the cost of forging such tracks in those days... The idea for steam powered locomotives probably originated with James Watt.

4. The fastest commercial trans in service are the German bullet trains -- they have reached over 300MPH and are in constant competition with the French TGV and Japanses Shinkasen Railways.

5. I don't know what a side rod is -- do you mean the piston ram on a steam locomotive? On a steam driven locomotive, the piston is colinear with the center of the drive wheels of the train.

There are several net locations for railways -- try TGV on a hot-bot or yahoo search.

Contribution from a reader
While it wasn't part of what I was looking for, I decided to have a look anyways, owing to my general fascination with steam locomotion. I am aware that this was never intended as a comprehensive answer, there are some parts of it that I would like to expand upon.

One such remark is that yes, trains nowadays do use gears, although not like the selectable gears in the transmission of a car. Although they are not the main method of transferring power from the prime mover (the diesel engine) to the wheel bogies/trucks, gears are used to transfer power from the electric drive motors in the trucks to the wheel and axle assemblies.

Also, while most steamers used main and side rods to transfer power mechanically from the pistons to the wheels, there were also several families of steam locomotives that used gears and drive shafts as the main method of power transmission. The main varieties of these engines were known as Shays (which had three steam cylinders arranged vertically on the right side of the offset boiler), Heislers (which had two cylinders in a Vee arrangement under the boiler), and Climaxes (which had one cylinder on each side of the boiler, and turned cranks attached to a large gear box under the boiler).

These engines all used gears and drive shafts to transmit power from the cylinders to the wheels, although the gears and drive shafts on the Shay ran down the right side of the locomotive while those on the Climaxes and Heislers ran down the center of the engine. Such engines were used in applications where raw pulling power, maneuverability and small size were needed at the expense of speed, such as small logging and industrial railroads. These engines had additional advantages due to the fact that because there were no large wheels permanently affixed to the chassis, they could maneuver around very tight track curvatures, since all the wheels were on pivoting bogies.

Additionally, because there were no pilot wheels or trailing trucks sharing the weight of the locomotive and tender, the entire weight of the engine was used to press the drive wheels to the rail. This enabled comparatively small engines to provide pulling power far superior to any conventional engine of equal size.

There were also engines that used gear-driven valves to control the admission of steam into the cylinders, but these designs were evolutionary freaks that never went anywhere.

Another remark that I have is about the post that contended that steam locomotive speeds were limited by the need to save wear on their rails. While it is certainly true that steam engines were hard on trackage, this wasn't really the main constraint on a locomotive's speed. The main constraint was the intended usage of the engine. Trackage was usually enlarged/adjusted/reinforced/improved to reflect the operating speeds of the trains and tonnage being moved. For an engine that was intended purely for hauling heavy freight trains at low speeds, small drive wheels (63" diameter or smaller) were most advantageous, because they gave maximum torque, you could fit a very wide, heavy boiler above them, and you could cram more of them under a boiler of any given length. However, small wheels necessarily limited the size of the counterbalances on the wheels, so running such engines at high speed did tend to beat the daylights out of the track, because the small wheels and associated connecting rods and running gear had to spin very, very quickly at such speeds. The general rule was the faster the engine was meant to go, the larger its wheels had to be. Passenger engines designed for speed could have wheels 80" in diameter or larger.

The trade off was that passenger engines made less tractive effort (pulling force), but this was all right because passenger trains tended to be lighter than freight trains.

Also, regarding item #5 of the answer above, down there at the bottom, a steamer's main rod is the big connecting rod that runs from the piston crosshead to the main crankpin, and the side rods are the smaller connecting rods that run from the main crankpin to the other drive wheels.