Those trains probably run on AC motors, because then they can use transformers to transfer power between circuits. Most likely, these trains use induction motors. To reverse the direction of the train, the engineer reverses the direction in which magnetic poles in the motors' stators circle the motors' rotors. When the poles reverse directions, the rotor has to reverse its direction, too, so that it chases those poles around in a circle.
The manufacturer assembles the magnet from hard magnetic materials. These materials are intrinsically magnetic (ferromagnetic) so that they have tiny magnetic domains inside. They are hard, meaning that these domains have great difficulty changing their magnetic orientations. As the final processing step, the finished magnets are exposed to an extremely strong magnetic field; so strong that it flips all of the domains into the desired direction. The domains become trapped in this new orientation and the magnet becomes permanently magnetized. Unless it is exposed to other very strong fields or excessive heat or shock, it will remain permanently magnetized indefinitely.
The tape recorder first represents sound (pressure fluctuations in the air) as electric current and it then represents that current as magnetization of a tape. It magnetizes the tape to various depths to represent the different amounts of current and it uses the direction of the magnetization to represent which way the current should flow. During playback, the tape recorder measures just how deeply and in what direction the tape has been magnetized and uses that information to recreate the current and the sound.
The term "dB" is a measure of power. It appears in many contexts, including sound power and audio signal power. Like the Richter scale used to measure the energy released by an earthquake, the dB scale is an exponential one—a sound that is 10 dB louder than another sound has 10 times as much sound power in it.
The term "BIAS" refers to a technique used to assist magnetic recording of weak audio signals. The magnetic particles on a tape's surface do not magnetize easily and need help when quiet sounds are being recorded. To provide that assistance, the tape recorder superimposes a strong, high-frequency "bias" signal on top of the weak audio signal. This inaudible bias signal allows the weak audio signal to influence the tape's magnetization. The characteristics of the bias signal must be adjusted to match the tape type.
The term "HX-Pro" probably refers to a variable bias techniques that prevents the bias signal from saturating the tape's magnetization and wasting some of the tape's dynamic range. (I'm less certain of this observation—please tell me if I am wrong and I'll fix this remark).
The term "Dolby Noise Reduction" refers to a collection of techniques for reducing high frequency noise on magnetic tapes. The higher the sound frequency, the smaller the patches of tape surface that are used to record each cycle of the sound. Since the recording occurs by magnetizing individual particles that are almost a micron long, the cycles of a high frequency sound do not use very many of the particles. A few miss-magnetized particles in each cycle can produce noticeable noise in the reproduced sound. To counter this noise, Dolby boost the volume of high frequency sounds during recording and then reduces their volume back to normal during playback. The noise caused by the particles is also reduced in volume and is less noticeable as a result. The different Dolby techniques refer to different filtering protocols, with C being an improvement over B, which was itself an improvement over A.
The term "20-bit LAMBDA Super-Linear converter" probably refers to a high performance Digital-to-Analog Converter (DAC). When a compact disc is played back, the audio signal must be converted from a stream of numbers into a smoothly varying electric current, which is then amplified and sent to a speaker. Turning each number into a current requires a DAC. The more carefully this DAC is built, the more perfectly the current passing through the speaker will represent the numbers on the disc and the recorded sound information. While most DACs work with only 16 bits, the one you mention provides 4 more bits of precision. However, the compact disc contains only 16 bits of sound information, so the 4 added bits must be created by some numerical analysis on the part of the compact disc player. This sort of signal processing may lead to reduction in noise during playback, but I wouldn't expect most people to be able to hear any difference.
The two quantities are related but they're not the same. If you think of a large magnet as made up of many tiny magnets all turned in the same direction, you can think of magnetic flux as strings that connect each tiny north pole to each tiny south pole. The large magnet effectively has many of the strings extending outward from its north pole and wrapping around to its south pole. The magnetic field at each location in space around the magnet is related to how many of these strings of magnetic flux pass through a small surface at that location. Near the poles of the magnet, the density of magnetic flux lines is high and so is the magnetic field. Far from the magnet, the density of magnetic flux lines is low and the magnetic field is weak.
It's true for both because permanent magnets are just a special material that has been magnetized. In fact, permanent magnets are often demagnetized more easily than other simpler materials. Anything that spoils the internal order of a material (heat or vibration) can demagnetize it.
The process of winding tape up on reels does damage its magnetism slightly. The adjacent layers of tape do interact with one another and they do cause the sound on one layer to appear on the adjacent layers. Fortunately, the effect is very subtle and takes a long time to appear so that the tape must remain tightly wound up for ages before you can hear the damage. Tapes don't age perfectly anyway because thermal energy slowly erases the magnetization, particularly in a hot environment.
A decade or two ago, it was important to match the power transistors used to control currents leaving an audio amplifier. If the transistor that controlled current flowing one direction through the speaker was significantly different from the transistor that controlled current flowing in the opposite direction, then the sound reproduction would be poor. That's because the current flows would be asymmetric and asymmetric currents lead to distorted sounds from the speaker. The most common measure of this sort of error is called "total harmonic distortion," an indication of how much power the amplifier puts into unwanted high frequency currents. Without carefully matched power transistors, an amplifier might put several percent of its power into these harmonic frequencies.
However, modern audio amplifiers generally use feedback techniques to correct for their own internal imperfections. They can compensate so well for mismatches in their components that total harmonic distortion has virtually disappeared from amplifiers. Amplifiers are still rated according to total harmonic distortion, but now it is rarely more than a few thousandths of a percent and depends more on the feedback techniques used than on the perfection of the power switching components. In short, the power transistors in modern amplifiers don't have to be matched well any more.
The coil in a microphone is attached to a movable surface that is pushed back and forth by the sound. Near the coil is a magnet so that, as the coil moves, the magnet induces electrical currents in it. Whenever a magnet moves past a coil of wire or a coil of wire moves past a magnet, a current is induced in that coil of wire.
As the current passing through the speaker's coil changes, the speaker cone moves back and forth toward or away from the speaker's permanent magnet. This moving cone pushes or pulls on the air, creating compressions and rarefactions that propagate through the air as sound.