If you check out the wikipedia page:
Transverse Mode
You'll see at the start of the second paragraph they say
"Transverse modes occur because of boundary conditions imposed on the wave by the waveguide"
This accounts for the discrepancy you have observed. Most diagrams of electromagnetic waves depict waves in free space, far away from any objects, and in that situation, you will have no electric or magnetic component in the propagation direction. Waveguides are (metal or fiber) tubes that confine an electromagnetic wave and force it in a particular direction. Since you have now introduced materials into the picture, things get more complicated, and you can have a non-zero electric and magnetic fields in the propagation direction.
Most E+M textbooks will have a section on waveguides, and these concepts figure heavily into fiber optics engineering.
what happens if the length of the feedline to this quarter wavelength transformer starts with the RF wave being not at a perfect division of the wave, e.g. 1/4, 1/2, 3/4 ? Does the length of the feedline to the quarter wave length transformer need to be a certain length too?
No. If the 1/4-wave transformer does its job, then the impedance looking in to the transformer (with the antenna loading the other side) will be matched to the feedline, and there will be no reflection returning to the generator, regardless of the length of the feedline.
if I am feeding a dipole antenna, do I similarly need to make sure that the feed line length is the correct length to allow for the current distribution to be at the correct points be nulls by adjusting the FEEDLINE LENGTH?
If you have a 300-ohm dipole, and feed it with a 300-ohm line, and drive it with a 300-ohm generator (as far as I know, such situations are rare), then the whole system is matched, there are no reflections returning the generator, and again it doesn't matter what the feedline length is.
For some other combination, you'd need to do the math and figure out whether the reflections are unacceptable for the generator or for the required system efficiency.
If you did have a mismatched system, you probably would not want to place the generator at a null of the current standing wave, as that is a point of high impedance, and it would be difficult to deliver power to the antenna. If the antenna is higher-impedance than the generator, you might want to place the generator at or near a null in the voltage standing wave. But most likely you'd still want some matching network to improve power transfer to the antenna.
Another example from ...- surely the length of the feeline should be specified for antenna design or am I missing something about it not effecting design if it is under a certain length.
This is an "inverted F" antenna. The placement of the feed at 2/5 of the distance from the shorted end of the antenna to the open end is intended to match the antenna impedance to the feedline. If this is chosen correctly, then there would be no reflections, and again the feedline length won't matter.
Best Answer
The antenna can't tell the difference between signals at all.
Even if an antenna is broadly tuned to a band, there could be many different transmissions within that band. It is only with tuning, filtering, mixing and finally decoding that the signals you are interested in can be differentiated from the rest.
For example, to receive simple AM broadcasts you could have a non-tuned antenna and feed the signals (all mixed up) into an RF amplifier and then into a mixer fed also by a carrier frequency of your choice (a local oscillator). When you mix the carrier signal with the modulated signals from the antenna you get product and difference signals. The difference signal turns out to be the audio you desire. You could start reading here.